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DIE CAST PROBLEM SOLVING

Publication #413

Scott Kirkman

Although great care has been taken to provide accurate and current information, neither the author(s) nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book. The material contained herein is not intended to provide specific advice or recommendations for any specific situation. Any opinions expressed by the author(s) are not necessarily those of NADCA. Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identification and explanation without intent to infringe nor endorse the product or corporation. © 2009 by North American Die Casting Association, Arlington Heights, Illinois. All Rights Reserved. Neither this book nor any parts may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher.

TABLE OF CONTENTS

I. Introduction …………………………………………………………………………

1

II. Variation and Basic Statistics ……………………………………………………… 3 III. Problem Solving Methodologies …………………………………………………

7

IV. 8D Step 1: Team Approach ………………………………………………………… 11 V. 8D Step 2: Describe the Problem ………………………………………………… 15 VI. 8D Step 3: Implement and Verify Interim Containment ………………………… 21 VII. 8D Step 4: Determine and Verify Root Causes ………………………………… 23 A. B. C. D.

Identify Potential Causes ……………………………………………………… Select Likely Causes …………………………………………………………… Is the Potental Cause a Root Cause? ……………………………………… Identify Alternative Solutions …………………………………………………

23 30 33 44

VIII. 8D Step 5: Verify Corrective Actions ……………………………………………… 45 IX. 8D Step 6: Implement Permanent Corrective Actions …………………………

49

X. 8D Step 7: Prevent Recurrence …………………………………………………… 51 XI. 8D Step 8: Congradulate Your Team ……………………………………………… 53 XII. Problem Solving Examples ………………………………………………………… 55 A. B. C. D.

Example 1: 2 Factor, 2 Level Full Factorial ………………………………… Example 2: 5 Factor, 2 Level Fractional Factorial ………………………… Example 3: 5 Factor, 2 Level Fractional Factorial ………………………… Example 4: 3 Factor, 3 Level Full Factorial …………………………………

55 56 60 68

XIV. Appendices …………………………………………………………………………… 73

Die Cast Problem Solving

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Die Cast Problem Solving

Chapter I INTRODUCTION The State of the Die Casting Industry The level of technology today in many die casting facilities is largely dependent upon the process knowledge that exists among the operators, managers, and process engineers within the facility. This knowledge is typically experiential in nature, and therefore, a common response to product defect problems has been to make significant process and die changes such as changes in gating, plunger diameters, die designs, etc. Although these changes may sometimes be effective, these changes frequently do not resolve the defect problem. The problem is a lack of industry skills and standards for analyzing process variation and optimizing critical process variables to minimize or eliminate product defect problems. Furthermore, when one tackles a problem by manipulating process factors to find the best process for a given defect problem, it is rare that the best process is found. This is because one typically changes only one process factor at a time until the process believed to be the best process is found. Since there are an infinite number of potential process combinations, finding the best process can never happen using this approach.

The Solution The lack of success in die cast problem solving is not likely due to a lack of interest or effort in solving problems. Rather, it is likely due to a lack in understanding the nature of variation, and the fact that the interactive nature of die casting makes solving process problems very difficult.

This Text This die cast problem solving text and the accompanying EC-413 course is unique and progressive in that it addresses variation thoroughly and covers the interactive nature of the die casting process by using problem solving tools that respect this interactivity. In addition, this book approaches problem solving using the Eight Discipline Problem Solving Process, which is required under QS-9000 certification and accepted under TS-16949 specification.

Die Cast Problem Solving

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Introduction

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Die Cast Problem Solving

Chapter II VARIATION AND BASIC STATISTICS Statistical Thinking “Statistical thinking is a philosophy of learning based upon the following principles: • All work occurs in a system of interconnected processes, • Variation exists in all processes, and • Understanding and reducing variation are keys to success.” (Special Publication, ASQC Statistics Division; Spring 1996).

Analyzing this statement in detail provides justification for the problem solving strategies proposed in this course… 1) “Learning” – Statistical methods enable us to learn more about the factors that control the quality of our process. The process knowledge gained using sound problem solving strategies may directly lead to technological improvements that provide significant quality and cost benefits. 2) “Work occurs in a system of interconnected processes” – In die casting, “interactive processes” may be a more appropriate term to use than “interconnected processes.” With that adjustment considered, the statement leads one to realize that the process and design factors that are required to make quality product must work in symphony together. In die casting, there is a significant interactive effect of all processes and design characteristics that come together at one instant to enable proper filling of the die within 0.005 to 0.200 seconds. 3) “Variation exists in all processes” – Variation occurs naturally in all things to some degree. The flattest, most perfect cut on the face of a diamond would appear very rough under our most highly powered microscopes, but this does not mean that the diamond is not of high value. It only illustrates that variation will always occur, and understanding the impact of the variation on product quality is what is important. 4) “Understanding and reducing variation are keys to success” – We must first understand what types of variation are important. Then we can find ways to reduce these significant process variations, which will likely lead to a decreased production of sub-standard product and thus an increased production of high-quality product.

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Variation and Basic Statistics

Average, Variance, Standard Deviation and Sigma Process variation is understood using the mathematical concept of variance. Variance is a squared number. Therefore, the variance that occurs in the thickness of a biscuit in cold chamber die casting is presented in inches squared (in2). Variance of a process is defined by the formula: n V = Σi [(X-bar – Xi)2] / (n-1) Where: Σ  is a symbol indicating the sum of the statement in the brackets [ ] from first sample i to the last sample n. X-bar is the average of all data points in a sample of the process. Xi is the individual value of each data point in the sample. n is the number of data points in the sample. Example: We sample 5 biscuits and find they measure 1.5 in, 1.3 in, 1.6 in, 1.4 in, and 1.7 in. We calculate X-bar as (1.5+1.3+1.6+1.4+1.7) / 5 = 7.5 / 5 = 1.5 in. Therefore, V = [(1.5-1.5)2 +(1.5-1.3)2 +(1.5-1.6)2 +(1.5-1.4)2 +(1.5-1.7)2] / (5-1) V = [0+0.04+0.01+0.01+0.04] / (4) = 0.10 / 4 = 0.025 in2

To put this into real terms that we can easily understand, we must take the square root of variance (V) to have a value in units that make sense to use. The square root of variance is called standard deviation (sd) when considering a sample of data from a larger population, and it is called sigma (σ) when considering all the data from a population. Note that sigma is a theoretical value and will not be used after this point in this text. For example: If our variance (V) is 0.025 in2 in our biscuit example, then the standard deviation (sd) is equal to the square root of 0.025 in2 or 0.158 in.

Normal Distribution The normal distribution is the probability density distribution, which defines most all types of variation in any process. A normal distribution appears as shown next:

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Die Cast Problem Solving

Variation and Basic Statistics Within the normal distribution curve, 68 percent of the variation falls within –1 to +1 standard deviation from the average; 95 percent of the variation falls within –2 to +2 standard deviations from the average; 99.7 percent of the variation falls within –3 to +3 standard deviations from the average; and 99.994 percent of the variation falls within –4 to +4 standard deviations from the average. We have accounted for all but 0.3 percent of the process defined by 3 standard deviations, therefore we typically use 3 standard deviations to define the normal variation of the process.

Relationship of Process Variation to Defect Variation As described earlier, standard deviation is the square root of variance. If we are analyzing the impact of process variation on the variation of a product defect, then we must consider the squared relationship as well. That is, if we have several process parameters whose variation contribute to the variation of a product defect, we must understand that reducing variation of one process parameter may not cause a significant reduction in the defect’s total variation. Remember that the standard deviation of the defect variation is equal to the square root of the sum of the squares of contributing variation from each of the process parameters. Therefore, we must consider the variation of all process parameters when utilizing an effective problem solving process. For Example: If: Sd = (Sc12 + Sc22 + Sc32+….)0.5 And: Three  parameters (Fast Shot, Metal Temperature, and Intensification Pressure contribute to a porosity defect variation as follows:

SFS = 2



SMT = 1



SIP = 2

Then: The total porosity defect variation is Sd = (22 + 12 + 22)0.5 = (9)0.5 = 3.  Through research and development we find that we can put a shot control valve on the shot end and reduce the Fast Shot standard deviation from 2 to 0.5. What will be the new porosity defect variation? The answer is Sd = (0.52+12+22)0.5 = (5.25)0.5 = 2.29. As you can see, the reduction in Fast Shot variation was extremely significant. However, the corresponding reduction in defect variation was not as significant.

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Variation and Basic Statistics Three important die cast problem solving pitfalls may be understood from the above example: 1) Several factors frequently affect a defect because of the interactive nature of the die casting process. 2) When several factors contribute to a defect’s variation, significantly improving one factor may not seem to have a significant effect on the defect. 3) Reducing  the variation of several parameters is often the only way to assure significant improvement. These pitfalls tend to result in unsuccessful problem solving efforts in die casting. Becoming aware of these potential pitfalls will make you a better problem solver.

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Die Cast Problem Solving

Chapter III PROBLEM SOLVING METHODOLOGIES There are several approaches to problem solving that have been offered to the manufacturing community. All of these approaches have some commonalities, which are: 1. 2. 3. 4.

Describe the problem. Determine and test potential root causes of the problem. Determine potential corrective actions. Implement corrective action(s).

A good problem solving method should include the above steps.

Eight Discipline Problem Solving Process The Eight Discipline (8D) Problem Solving methodology was developed by the Ford Motor Corporation. This methodology includes four steps that are not always used in other methodologies. These steps are: 1. Use a team approach. (8D step 1) Ford thought that a team approach to problem solving was superior to individual efforts. 2. Implement and verify containment. (8D step 3) This step is to assure that defective product does not get to the customer during the problem solving process. Therefore, once a company becomes aware of a defect, they should find a way assure that it is contained within the manufacturing facility where it is manufactured. 3. Prevent recurrence. (8D step 7) This step is to assure that a problem does not come back after time. 4. Congratulate the team. (8D step 8) This step is to promote team oriented problem solving by recognizing those who are involved. Since the 8D format has been adopted as the preferred problem solving methodology under the QS-9000 certification, this course and text will follow the 8D steps.

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Problem Solving Methodologies

Team Oriented Problem Solving While Ford created the 8D process, they also developed the Team Oriented Problem Solving (TOPS) process to work along with 8D. TOPS is a method designed to optimize the effectiveness of teams. Some of the TOPS techniques will be utilized in this course.

Eight Phase Problem Solving The Eight Phase (8 Phase) problem solving process is very similar to 8D except that teaming is not necessarily utilized, and other steps are not addressed in as much detail. Since 8D is the better-accepted approach and since the approaches are so similar, 8 Phase will not be referred to within this course.

Dorian Shainin Dorian Shainin is a problem-solving “Guru” who developed his statistical engineering methodology while working at Hughes Aircraft. His methods are still being used significantly within General Motors and some of his methods will be applied in this text.

Taguchi Taguchi, a Japanese problem-solving “Guru”, developed a non-interactive design of experiments methodology. His methods have been successfully used in non-interactive manufacturing processes for many years. However, his methodologies are of little use in the die casting industry due to the interactive nature of die casting.

Box, Hunter, and Hunter Box, Hunter, and Hunter, statistics professors at the University of Wisconsin – Madison, developed fractional factorial experiment designs that may be formatted to respect interactions within the die casting process. These types of experiments are utilized in this course in addition to other methods from Box, Hunter, and Hunter.

This Book The uniqueness of this book lies in that it is specific to the interactive nature of die casting. We consider a variety of existing problem solving tools such as 8D, Shainin, Taguchi, and Box, Hunter, and Hunter. The specific problem solving tools selected are those that work well in reducing interactive die casting problems. The new problem solving format, outlined below, is linked to the 8D steps for ease of application and understanding.

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Die Cast Problem Solving

Problem Solving Methodologies

Die Cast Problem Solving

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Problem Solving Methodologies

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Die Cast Problem Solving

Chapter IV 8D STEP 1: TEAM APPROACH In general, teams have not been well utilized in the problem solving process in die casting, and therefore, are an important topic of discussion in this text. Teams are an effective and justifiable means of solving problems, and if employee involvement a goal, team oriented problem solving is the answer.

Benefit of Knowledge The most significant benefit of utilizing teams in the problem solving process is the cumulative knowledge that teams are capable of providing. By having a well-rounded team composed of people with the required product, process, and customer knowledge, problem solving is most likely to be effective.

Benefit of Employee Buy-in Beyond the obvious benefit of solving a product defect problem, teams may have a significant benefit with regard to employee buy-in toward manufacturing improvement. Since operators and other floor employees do not always directly see the benefits of their efforts, they often become disinterested in involvement in improvement activities. By effectively involving die cast floor employees in teams, employees become more aware of the benefits of their efforts and more satisfied with their employment.

Taking Advantage of the Experts The most important aspect of teamwork is to involve the people who understand process variation the most. Your first thought may be to involve the process engineers heavily in problem solving, however, it is the machine operators who likely understand process variation the most. The machine operators watch the process far more than anyone else does. They see how it changes over time. Furthermore, they are the experts when it comes to ideas regarding what may cause the process to vary over time. Not utilizing the expertise of machine operators in problem solving efforts is the biggest roadblock to team development in the die casting industry. Learning to involve operators in problem solving teams is the key to team success.

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8D Step 1: Team Approach

Team Development Guidelines The following guidelines should be used in determining team membership: 1) Each team member must directly gain from the success or lose from the failure of the problem solving project. People who do not gain or lose from their efforts should not be involved. 2) Each team must consist of at least four members and no more than eight members. If the team has too few members, you may not get buy-in for a solution. If there are too many members, you may not maintain involvement. 3) Each team member must have time, which is understood by his or her manager, that is allocated to work on tasks related to the team. If managers and supervisors do not allocate this time or are not aware of the need to spend time on the project, tasks will likely not be done. 4) Each team should have at least one operator, one process or product engineer, one quality engineer or inspector, and one manager. The manager should act as the team facilitator and break down barriers to problem resolution. If more members are to be included in a team, add operators, possibly trimmers, or others that have something to gain or lose from the completion of the project.

Brainstorming Brainstorming is a team problem solving tool that is critical to success in problem solving. The goal of brainstorming is to attain the most creative and effective ideas toward the resolution of a problem. To get these types of ideas, brainstorming should be conducted in the following manner: 1) Discussions should be enthusiastic and people should be commended openly for all ideas. Ideas that appear silly or outrageous may not seem valuable at first, however, these types of ideas may lead to creative solutions. The facilitator should promote these approaches. 2) Allow only one person to speak at a time. The facilitator should control who speaks so that all have the opportunity to express their thoughts. 3) Do not ever criticize, evaluate, or compare one idea to another. Just write them all down. The facilitator should write down ideas and assure that the group follows this rule. 4) The facilitator should make sure the discussion is limited to the problem described.

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Die Cast Problem Solving

8D Step 1: Team Approach

Storyboard Brainstorming Storyboard Brainstorming is a team tool to be used for brainstorming when: • The sequence of events in the process is not necessarily clear. • The point at which defects occur is not clear. • There are members within the group who are not likely to become involved or there are members who will tend to control the problem solving process. To use Storyboard Brainstorming follow these steps: 1) For each process step or operation, have each team member note potential causes of the defect that could originate in each step. Use Post-ittm notes. 2) P  ut these potential causes of the defect on a board or wall in sequence of the process. 3) Follow brainstorming rules otherwise. The benefits of storyboard brainstorming are as follows: • It enables structured brainstorming for defect resolution of multiple operation processes. • It enables the group to learn about the entire process. • It minimizes the impact of dominant group members and promotes the involvement of typically uninvolved employees.

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8D Step 1: Team Approach

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Die Cast Problem Solving

Chapter V 8D STEP 2: DESCRIBE THE PROBLEM Definition Statement The definition statement is critical to beginning an effective problem solving project. Once a problem solving team is created, coming up with a commonly understood definition statement is the first task for the team. Once developed, the definition statement should assure that the team directly attacks the cause of the problem defined in the definition statement. Philosophically speaking, the statement, “A problem well described is a problem half solved,” describes the importance and benefit of a good definition statement. The definition statement should have three separate components. It should begin with the part number or description. The statement should then clearly define the defect or symptom. Once the problem solving project is complete, the statement will conclude with the third part, which is the proven cause of the defect or symptom. This sounds very simple, however, it is critical to proper team-based problem solving.

Pictograph or Defect Pictures The pictograph is a picture that is used to visually describe the location of a defect. The pictograph should be used with the definition statement to document and define a defect. The best means of visually illustrating a defect is having the actual products with defects present at the problem solving meeting. However, the pictograph is required for long-term defect and problem solving documentation. Digital photos are a very good way to describe a defect if an effectively clear digital camera is available. Often the defects are not easy to see on photos.

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8D Step 2: Describe the Problem

Defect Ranking System The problem description and pictograph help define the defect problem for resolution. A ranking system must be established to measure the defect problem. The best ranking system is a gage of some sort. However, almost all die casting defect problems are subjective in nature and cannot be measured with a standard gage of any sort. Examples of subjective die casting defects include non-fill, surface appearance, porosity, blisters, warping, stains, and flash. Therefore, we have to create our own gage that we call the “defect ranking system.” The following steps must be followed to create a defect ranking system: Step 1: Determine the number of rank levels.  se from 2 to 10 defect rank levels. Use more levels for more costly problems. U Do not pick so many levels that determining rank level is too difficult. Knowledge of determining the number of rank levels improves with experience. Step 2: Select a balanced sample of good parts and defective parts that ranges from the very best defect level to the very worst.  balanced sample does not infer a normal sample because a normal sample A of product may have only a small percentage of defective products. The number of castings in the balanced sample should be from 5 to 20 times the number of rank levels. Step 3: Place all the parts in a row from bad to good. Step 4: Divide the row of parts into several fairly equal groups.  he number of groups is equal to the number of rank levels chosen in Step 1. T Make sure that the good/bad boundary is between two of your groups. Your groups will be numbered 0, 1, 2, 3…etc. Step 5: Select the boundary samples by picking the part that best falls between the individual groups. One boundary sample will be the good/bad boundary. This boundary sample should be the part that is most difficult to determine its acceptability to the customer. Your boundary samples will be numbered 0.5, 1.5, 2.5…etc. The number of boundary samples will be one less than the number of groups. These boundary samples are now your gage. They should be protected and preserved. Step 6: Complete an Iso-Plot or a Gage Repeatability and Reproducibility (Gage R&R) study to test the validity of your gage.  se an Iso-Plot for most situations, however, you may want to use a Gage R U & R for a more deterministic gage evaluation method. Note that you may be required to use a Gage R & R if you use your gage as a product validation tool under QS-9000 or ISO-9000 requirements.

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Die Cast Problem Solving

8D Step 2: Describe the Problem

Iso-Plot An Iso-plot is a tool to compare: 1) two different types of gages, 2) two identical gages, 3) two people using a gage, or 4) any type of comparison of gages. The Iso-plot is a Dorian Shainin tool that is shown in the example below:

The following steps are used to create an Iso-plot: 1) Select a sample of parts for usage in your study. (20 to 50 parts) 2) Measure each part using two gages, people, or time frames. 3) Chart the two gage methods with one method on the Y-axis and the other on the X-axis. 4) Plot one point for each part in your sample. 5) Sketch the shape that represents the extremity of the variation. The shape will be oblong like a football at a 45 degree angle. The Iso-Plot is evaluated by measuring the following: • Process variation is determined by measuring the length of the plotted football shape. • Gage variation is determined by measuring the width of the plotted football shape. • Repeatability/reproducibility percentage is equal to the gage variation divided by the process variation. • Accuracy is determined by calculating the difference of the averages of each method. • The accuracy percentage is equal to the accuracy divided by the process variation. • A good repeatability/reproducibility percentage value is below 30 percent. • A good accuracy value is below 10 percent.

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8D Step 2: Describe the Problem

Gage Repeatability and Reproducibility Gage Repeatability and Reproducibility (Gage R & R) is a statistical evaluation tool to compare two people or two gages measuring the same parts. Gage R & R is most commonly used for measuring gage capability for critical casting dimensions. The standard under QS-9000 in this case is a Gage R&R percentage of 10 percent. When used on non-critical characteristics, the standard requirement is 30 percent. We typically follow the 30 percent standard for gage capability because subjective defects and our defect ranking system are not hard gages. However, you may desire to achieve higher gage capability for difficult-to-resolve or high-cost defects. The following describes how to complete a Gage R & R study: Step 1: R  andomly select 5 to 10 parts from the balanced sample of parts. Select more parts for defects that are more difficult to evaluate. Step 2: Using the defect ranking system boundary samples, measure the defect level for all selected parts using two or three different people. These should be the primary people accustomed to evaluating product on a day-to-day basis. Step 3: Measure the same parts in exactly the same way as in Step 2 over a period of one or two more days. Step 4: Complete the table below with the results of the measurements. Day 1

Day 2

Part Inspector 1 Inspector 2 Average Range Part Inspector 1 Inspector 2 Average Range Grand Avg.

1 2 3 4 5

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1 2 3 2 4

2 2 3 2 5

1.5 2 3 2 4.5

1 0 0 0 1

1 2 3 4 5

1 2 4 2 4

Die Cast Problem Solving

1 2 3 2 5

1 2 3.5 2 4.5

0 0 1 0 1

1.25 2 3.25 2 4.5

8D Step 2: Describe the Problem Calculate the following statistics from the above data: Inspector 1 Average = average of all data points from Day 1 and Day 2 = 2.5 Inspector 2 Average = average of all data points from Day 1 and Day 2 = 2.7 Parts (n) = 5 Trials (r) = 2 (for 2 days) Inspectors (e) = 2 Grand Mean Average = average of all inspectors = 2.6 Grand Range Average = sum of all ranges/(n x r) = 4/(5 x 2) = 0.4 Difference Between Inspectors = absolute value of (Inspector 1 Average – Inspector 2 Average) = 0.2 Maximum Part Range = High Grand Average – Low Grand Average = 4.5 – 1.25 = 3.25 Calculate Gage Capability: Error Between Inspectors (Repeatability) = Grand Range Average x K1 = 0.4 x 4.56 < K1 from constant table in Appendix 1. = 1.824 Error Within Inspectors (Reproducibility) = [(Diff. Bet. Insp. x K2)2 – (Repeatability2/(n x r))]0.5 < K2 from constant table in Appendix 1. = [(0.2 x 3.65)2 - (1.8242/(5 x 2))]0.5 = 0.447 Repeatability & Reproducibility (R&R) = [(Repeatability)2 + (Reproducibility)2]0.5 = [1.8242 - 0..4472]0.5 = 1.878 Part Variation = Max Part Range x K3 < K3 from constant table in Appendix 1. = 3.25 x 2.08 = 6.76 Total Variation = [(R&R)2 + (Part Variation)2]0.5 = [(1.878)2 + (6.76)2]0.5 = 7.016 % Repeatability = 100 x Repeatability/Total Variation = 100 x 1.824/7.030 = 26.0%

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8D Step 2: Describe the Problem % Reproducibility = 100 x Reproducibility/Total Variation = 100 x 0.447/7.030 = 6.4% % R&R = 100 x R&R/Total Variation = 26.8% The above would be considered an acceptable gage since the Gage R & R % is less than 30%. Microsoft Excel forms for completing Gage R & R studies are included with the NADCA information available on-line and a Gage R & R calculation template is displayed in Appendix 2.

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Die Cast Problem Solving

Chapter VI 8D STEP 3: IMPLEMENT & VERIFY INTERIM CONTAINMENT To assure that defective product does not get to the customer, the 8D problem solving methodology requires that some sort of defect containment be implemented. This defect containment is only an interim measure, which typically requires extra inspection activity, to find product defects within the die cast facility. Since containment is required under the Eight Discipline process and is costly, it should motivate the die caster to rapidly resolve the defect problem. The extra inspection may also provide an opportunity to gather quality data that is difficult to gather without inspection. This data may be very useful during the problem solving process.

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8D Step 3: Implement & Verify Interim Containment

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Die Cast Problem Solving

Chapter VII 8D STEP 4: DETERMINE & VERIFY ROOT CAUSES Step 4 in 8D problem solving, which is “Determine and Verify Root Causes,” is the meat of any problem solving effort. It is broken down into four sub-steps: 1) identify potential causes, 2) select likely causes, 3) test to determine if the potential root cause(s) is a root cause, and 4) select potential solutions to eliminate the root cause(s).

A) Identify Potential Causes Clue Generation The tools we will use to identify potential causes are called clue generation tools. Each of these tools is designed to provide more data, or clues, to determine what is causing a product defect. For any defect problem, it is advisable to use multiple clue generation tools.

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8D Step 4: Determine & Verify Root Causes Chronic Cause vs. Special Cause Problem Analysis To identify potential causes, you must first determine whether the defect problem is a “chronic cause” or a “special cause” defect problem. A chronic cause problem is a problem that is always there. In other words, the random normal variation of the process may cause the problem or defect to occur at any time. A special cause problem is a problem that comes and goes entirely due to human or mechanical intervention. We must determine if the problem is chronic or special cause in order to determine which tools to use in the problem solving project. If you are not certain whether a defect is chronic or special cause, you must use tools for both approaches until you ascertain the problem as one or the other. From this point forward, each tool described will be defined as a good chronic cause tool or special cause tool for problem resolution. TOPS Is and Is Not Questions The Ford Team Oriented Problem Solving (TOPS) Is and Is Not question methodology is an excellent tool for beginning to understand special cause defect problems. This is because these questions assist a problem solving team in exhaustively comparing the current problem situation with other parts, dies, designs, times, situations, or processes where the problem may not occur. For example, two similar die castings exist in your company. You find that one has a product defect problem. Using the Is and Is Not questions will enable you to more accurately pinpoint the reason(s) for the problem by comparing the two parts’ processes, dies, designs, etc. until you have generated an idea of what the differences are among the parts. These differences then become clues as to what the root cause(s) of the problem might be. Below you will find the Is and Is Not Questions for use in die cast problem solving:

IS

1. Which part(s) has the defect?



IS NOT

Which similar part(s) could have the defect, but does not?

2. What is the defect?

What could be the defect, but is not?

3. Where specifically do you see the defect(s) on the casting?

Where specifically could you have seen the defect(s) on the casting, but did not?

4. Where geographically and when in the process flow do you first see the defect?

Where geographically and when in process flow could have you first seen the defect, but did not or could not?



5. When in time did you first see the defect(s)? (hr. / day / mo. / yr.)

When in time could you first see the defect(s), but did not?



6. Since you first saw the defect, when have you seen it again? Can you observe any trends or patterns?

Since you first saw the defect, when could you have seen the defect again, but did not? Can you observe any trends or patterns?

7. What is the current state of the defect?

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What state could or should the defect be in now, but is not? Is it getting better? Worse?

8. How big is the defect in terms of percentage, How big could the defect be, but is not? dollars, people, time, or other resources?

Die Cast Problem Solving

8D Step 4: Determine & Verify Root Causes Defect Tally Sheet The Defect Tally Sheet shown below is a tool that may be used for understanding the occurrence rate of multiple defects. It is an effective tool to determine whether a defect is a special cause or chronic cause defect. It also can help you determine if the defect rate(s) change from hour to hour or shift to shift. Production employees should use the Defect Tally Sheet to record the number of defects that occur each hour during the shift. Defect Tally Sheet Day

Shift

1

1

2

3

1

2

2

3

Hour 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

Defect 1

Defect 2

Defect 3

Die Cast Problem Solving

Defect 4

Defect 5

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8D Step 4: Determine & Verify Root Causes To analyze the defect tally sheet you must create a probability chart (p chart) for each defect. You may then easily understand the average defect rate and variability for each defect studied.

Process Flow Diagram The process flow diagram is a tool to resolve special cause defects. It is only valuable when the defect is not created in the die casting process, but occurs at some process step after die casting. It is especially useful for handling damage defects, as shown in the example, because you can relate the defect rate with each process step. Process Flow Diagram Batch Sizes

Manufacturing Operations

Quality Checks/Audits

Defect Mode

3,000

Die cast

Operator hourly Quality shiftly

Handling damage 1%

10,000

Tumble

300

Thermal Deburr

5,000

Cleaning

5,000

Plating

5,000

Washing

Quality audit

20,000

Ship

100% sort

1

Assemble

Handling damage 6% Quality audit

Handling damage 8% Handling damage 12% Scrap 12%

Multi-Vari Study The Multi-Vari study, developed by Dorian Shainin, is the most valuable clue generation tool for chronic cause defect problems. The purpose of the study is to determine the “Time Mode of Variation” of the product defect problem. The “Time Mode of Variation” is how a defect varies over time. For example, if the Multi-Vari shows that the defect varies from piece to piece, then the clue is to look for causes that vary from piece to piece. If the defect would vary from shift to shift, then the clue is that something is changing from shift to shift. In summary, the reason that the Multi-Vari study is so valuable is that it can significantly narrow the number of potential causes of a product defect problem. The procedure for completing a Multi-Vari study is as follows:

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8D Step 4: Determine & Verify Root Causes 1) Determine the number of castings to be collected each hour and each shift, as well as the length of the study in days. Make sure castings are collected during all shifts. Difficult to resolve or expensive defects: 4 pieces/hour, 4 hours/shift, and 4 days/study Moderately easy to resolve or moderately expensive defects: 3 pieces/hour, 3 hours/shift, and 3 days/study 2) Collect castings under normal process conditions. Assure that operators on all shifts do not change the way that they run the process during the study. This may be done by either collecting castings without their knowledge, or preferably by involving them in the problem solving process so they appreciate the purpose of the study. Assure that castings are collected in consecutive order over consecutive hours, shifts and days. 3) Process the castings to the point where the defect is typically found. 4) Rank the castings using your defect ranking system. 5) Chart the results with the defect rank on the Y-axis and the casting collection order on the X-axis. 6) Evaluate the results visually or statistically. The following are examples of the results of two Multi-Vari studies: The first example (on the cover of this book) shows a complete Multi-Vari chart. To analyze this chart, you must compare the amount of variation within each potential time mode of variation (i.e., piece-to-piece, hour-to-hour, shift-to-shift, and day-to-day). On this chart, it appears that piece-to-piece variation is most significant, however shift-toshift variation also appears to be somewhat significant.

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8D Step 4: Determine & Verify Root Causes In contrast, the charts in the second example show a Multi-Vari study broken down into individual piece-to-piece, hour-to-hour, shift-to-shift, and day-to-day charts.

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8D Step 4: Determine & Verify Root Causes T.O.P.S. Is and Is Not Differences As discussed earlier in the text, the Team Oriented Problem Solving Is and Is Not questions generate answers that may be used to generate clues. The differences are obtained by comparing the answers to each Is and Is Not question, and then brainstorming explanations for the differences in answers. Once brainstorming of these differences is completed, you should have created a list of differences that explain each set of Is and Is Not questions. There should be at least one difference brainstormed for each set of questions. A documentation sheet for the Is and Is Not Differences is included in Appendix 3. Cause and Effect Diagram (Ishikawa) The Cause and Effect Diagram, shown below, is a basic tool used to brainstorm potential causes. This tool may be used for special and chronic cause defects, but is typically more valuable for special cause defects. It is especially valuable in assuring that all possible reasons for a problem are identified. For example, assume that your group brainstorms different factors that operators may change from shift to shift because your product defect problem is varying from shift to shift. Your group may forget to consider that your measurement system may change because you now have different inspectors looking at the defects from shift to shift. Using the Cause and Effect Diagram would have allowed your group to consider this potential cause when they may not have otherwise. To use the Cause and Effect Diagram, write the symptom or problem description in the box at the far right. Then create categories for the six M’s (Man, Machine, Method, Material, Measurement, and Management). Finally, brainstorm, with your problem solving team, potential causes that would fall under each of the six categories.

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8D Step 4: Determine & Verify Root Causes

B) Select Likely Causes The purpose of the previous section, “Identify Potential Causes,” is to develop clues regarding the cause of a defect and then brainstorm potential causes using these clues. This section will provide tools to narrow down the potential causes into a smaller set of likely causes. The tools identified here are team tools designed to enable the problem solving team to logically eliminate unlikely potential causes. TOPS Is and Is Not Theories From the TOPS Is and Is Not Differences, your team should brainstorm theories that explain the differences. The team should attempt to brainstorm multiple theories for each defined difference in order to explain the root cause of the differences. The same theories may be used to explain several differences. These multiple theories are then considered potential root causes to the defect problem. A documentation sheet for theories is available in Appendix 4. TOPS Theories/Differences Matrix From the TOPS Is and Is Not Theories and Differences, your team should now develop a Theories/Differences Matrix. This matrix is used to assist you in rating the relative significance of the theories that were brainstormed so that you may decide which theories to test and/or implement.

Differences Theories T1 T2 T3 T4 T5 T6 T7 T8 T9 T10

D1

D2

D3

D4

D5

D6

D7

D8

Score

In the matrix shown above, your team decides if the theory explains, partially explains, or does not explain the difference noted for the Is and Is Not Questions. If the theory fully explains the difference, then enter a 1 in the corresponding cell. If the theory partially explains the difference, enter a ½ in the cell. If the theory does not explain the difference, enter a 0 in the cell. Take the sum of each row to determine the score of each theory. Those theories with the highest scores are the likely root causes. Addressing these root causes in order of score should improve or eliminate the product defect problem most effectively.

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8D Step 4: Determine & Verify Root Causes In the example below, questions five and seven were not answered fully so they did not have differences (D5 and D7) and theories. Seven theories were brainstormed. When they were compared to the differences, a score was developed for each theory. From these scores, Theory 2 (T2) would be the most significant theory to try first. The other theories would be tested in descending score order until the defect is satisfactorily resolved. Selecting Likely Causes for Chronic Cause Defects

Differences Theories T1 T2 T3 T4 T5 T6 T7 T8 T9 T10

D1 0 1 0 0 1/2 1/2 1

D2 1/2 1/2 1 0 1/2 0 0

D3 0 1 1 1 1 0 0

D4 1 1 1/2 0 1/2 1/2 0

D5 N/A N/A N/A N/A N/A N/A N/A

D6 0 0 0 1 1/2 0 1/2

D7 N/A N/A N/A N/A N/A N/A N/A

D8 0 1 1 1/2 0 1/2 1/2

Score 1½ 4½ 3½ 2½ 3 1½ 2

Likely causes for chronic cause defects also need to be determined. Brainstorming using the clues that we have generated will accomplish this task. If you have done a complete job in clue generation, the brainstorming should be fairly easy. First, the team leader or facilitator should distribute or display all the information found during clue generation tools. Using the clues, the team members should brainstorm possible causes. The possible causes are typically process variables that explain the chronic variation. The leader or facilitator should document all the ideas from brainstorming. The next phase of chronic cause problem resolution will be to conduct a designed experiment. Designed experiments containing more than five process variables are cumbersome in the die casting process; therefore, we must reduce the number of potential causes to five or less at this point. To reduce the number of process variables below five, the problem solving team should first collectively discuss the importance of each process variable in its relation to the defect. It is important to consider the clues that your team has generated during this discussion. If the team cannot reduce the number of process variables below five during this process, a correlation analysis must be used.

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8D Step 4: Determine & Verify Root Causes Correlation Analysis A correlation analysis is a rarely used but is a valuable tool in problem solving efforts. The only time when this analysis must be used is when more than five variables remain after brainstorming. The goal of using a correlation is to find which variables vary with the defect, and eliminate the variables from consideration that do not vary with the defect. To complete a correlation study, collect a small sample of castings over the time mode(s) of variation established in the multi-vari study along with the process variable information. Then, mathematically calculate your correlation using the Excel correlation spreadsheet provided within the NADCA on-line files. To evaluate a correlation study, compare the calculated correlation values for all measurable process variables to the defect rank level. The value for a correlation will be between -1 and 1. If the value is a positive number, it means that you have positive correlation. A positive correlation indicates that when the defect level is lower, the process variable level is lower, and when the defect level is higher, the process variable level is higher. If the correlation value is negative, it means that when the defect is lower, the process variable level is higher and vice-versa. The closer the correlation value is to 1 or -1, the stronger the correlation. A correlation value close to zero indicates a weak correlation. Therefore, the process variables with correlation values closer to zero are less important in your problem solving effort. You should eliminate process variables from consideration until you have five or fewer variables remaining. The following example illustrates how to interpret a correlation:

Correlation Analysis

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Porosity Level 6 5 1 4 7 6 2 0 3 8

Fast Shot Velocity 84 84 80 83 85 85 81 80 81 85

Impact Pressure 2120 2120 2150 2130 2100 2110 2140 2150 2150 2110

Vacuum Time 4 5 5 5 1 2 5 1 2 5

Intensifier Rise Time 3 4 1 2 3 1 0 0 1 5

Correlation

0.96 Positive Correlation Significant

-0.93 Negative Correlation Significant

0.05 Positive Correlation Insignificant Eliminate from Test

0.81 Positive Correlation Somewhat Significant

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8D Step 4: Determine & Verify Root Causes

C) Is the Potential Cause a Root Cause? The most critical part of problem solving is to determine whether your theories or process variables selected truly have an effect on the product defect problem you are trying to resolve. At this point, if we are resolving a special cause problem, we have theories that appear to explain the reason for the defect. If we are resolving a chronic cause problem, we have selected five or fewer process variables that appear to fit the clues that we have obtained on our product defect problem. Now we have to perform a test to see if we can “turn the defect off” and “turn it on” with these theories or process variables. Special Cause Defects The advantage of special cause problem solving is that you can easily and independently test your theories in attempt to resolve the problem. To complete a test on the theories, you should first baseline your defect level before the test. Then you should implement the change proposed by the highest scoring theory from the Theories/Differences Matrix. Finally, evaluate the change in the defect level. If an improvement is seen, this change should be permanently implemented, given that the change is cost effective. If the defect is totally eliminated, you need not implement any more theories. However, if some defect remains, you should try your other theories in order of score until you have exhausted your theories or you have eliminated the defect. Interactive Experimentation – Importance of Interactions Die casting is fairly unique among manufacturing processes. Along with injection molding, these are the only processes where tens to hundreds of process variables must work in harmony to produce a product that goes from raw material to finished product in a fraction of a second. This fact is what makes understanding process interactions imperative to die casters. The illustration below gives you an idea of how often interactions occur.

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8D Step 4: Determine & Verify Root Causes An interaction is when two or more process factors work together to affect a product defect. Interactions are independent of the individual effect of each process parameter involved. For example, assume we have two process variables, fast shot speed and die temperature, that both significantly affect porosity on a given casting. The parameters both affect porosity independently. This is not an interaction because they do not work together to affect porosity. When we test process factors in an experiment, we will test each factor at two or three levels. Assuming a two-level experiment is being done, an interaction is when the defect result differs when the two process factors are at the same level versus when they are at different levels. We will learn more about interactions in the examples experiments in Chapter 12 (Problem Solving Examples). Examples of interactions: The following IS NOT an interaction: Fast Shot Velocity 1 2 1 2

Die Temperature 1 1 2 2

Casting Rank 0 1 2 3

Die Temperature 1 1 2 2

Casting Rank 0 1 3 2

The following IS an interaction: Fast Shot Velocity 1 2 1 2 Blocking Blocking is a powerful tool in designed experimentation. Its value lies in that it reduces unexplained variation that could be caused by known process variables that are not included in the designed experiment. Thus, when conducting an experiment, blocking allows the effect of the experimental variables to be more apparent. When statistically evaluating your experiment, proper blocking will raise the statistical confidence of your experiment. The use of blocking is necessary because some process variables may vary with the time mode of variation and are not possible to control in the long term due to cost or lack of technology. Examples of such process variables in die casting may include die water temperature, plant ambient temperature, air pressure, or operator variation. Before conducting an experiment, any of the selected process variables that are not possible to control in the long term should be considered blocked variables.

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8D Step 4: Determine & Verify Root Causes The blocked variable(s) must be constant during the experiment. Blocking is accomplished by holding the blocked variable(s) at a nominal value during the experiment, or by waiting for the nominal value to occur before collecting castings. For example, assume you have cycle time variation because you have a manually operated machine. To block for cycle time, you should use a stopwatch to carefully time the machine to make sure that the cycle rate is the same during the experiment. If you wanted to block for fast shot velocity, you might wait until you measure the nominal value on a process monitoring system to collect castings for the experiment. Randomization Even after clue generation and several effective team meetings, you will likely still have process variables that the team did not consider that cause some variation in your defect. To minimize the effect of these factors during an experiment, we must randomize the order of the experiment. In order to realize the importance of randomization, we must consider the situation where we do not randomize. For example, assume we complete a two-factor, two-level experiment. Factor 1 is Fast Shot Velocity and Factor 2 is Intensification Pressure. Fast Shot Velocity will be tested at 90 and 100 inches per second and Intensification Pressure will be tested at 1200 and 1500 pounds per square inch. The experiment would appear as follows: Treatment 1 2 3 4

Fast Shot Velocity 90 IPS 100 IPS 90 IPS 100 IPS

Intensification Pressure 1200 PSI 1200 PSI 1500 PSI 1500 PSI

Assume that an air line blows on a nearby trim press sometime between treatments 2 and 3 of the experiment, and the machines air pressure drops from 100 PSI to 25 PSI for the duration of your experiment. This loss of air pressure causes your die spray to no longer atomize, and therefore your die temperature changes significantly. You then analyze the results of your experiment. The castings show that you have significant porosity on the castings from treatments 3 and 4, but treatments 1 and 2 are much better. Is this porosity difference due to the Intensification Pressure or is it due to the air pressure drop? You will never know because you did not randomize the experiment. To effectively randomize the experiment, the order of your experimentation should not have any patterns that would allow other variation to have a detrimental effect on the experiment. The best way to randomize is to use the random number tables supplied in each Excel experiment spreadsheet file. The random number table will change every time that you use the software. Therefore, to use the table, begin at the upper left corner. The first number is the first treatment that should be conducted. The number to the right should be the second treatment conducted and so on until all treatments in the experiment are accounted for. If you have a duplicate treatment number, ignore it. If you complete the first row without completing the experiment, go to the second row.

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8D Step 4: Determine & Verify Root Causes Three-Level versus Two-Level Experiments We have the choice of running an experiment with two parameter levels or three parameter levels for each process variable. The advantage of two-level experiments is that they are much quicker to complete and they allow you to use up to five process variables. The disadvantage of two-level experiments is that they only indicate a better or worse process. Thus, you do not know which is the best process. The advantage of three-level experiments is that you are able to understand much more about the process. A three-level experiment, when used properly, can enable quick process optimization. The disadvantage of three-level experiments is that you may only use up to three factors in the experiment and the experiments are very time consuming. For example, a three-level experiment with three factors requires 27 treatments. A two-level experiment with the same factors only requires eight treatments. The following chart illustrates the benefit of three-level experiments:

Factor Level Selection The most significant reason for the lack of success in designed experimentation for most experimenters is that factor levels are not selected properly. For a two-level experiment, the basic rule is that factor levels should be set at plus and minus three standard deviations from the current nominal process setting. If process monitoring equipment does not exist for the process factor, then the rule is that the factor levels should be set at a small increment above and below the current setting. For a three-level experiment, use the same rules except use the current setting as the third level. The following chart illustrates the above concept:

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8D Step 4: Determine & Verify Root Causes Confounding In fractional factorial designed experiments, some combinations of factors are not tested. When these experiments are used, the intent is always to assume higher level interactions or sometimes all interactions do not exist. However, when fractional factorial experiments are conducted, these interactions may occur. When these interactions occur in fractional factorial experiments, the high level interactions are confounded with main effects or lower level interactions. For example, when a 25-1 fractional factorial experiment is evaluated, the result of a main effect is confounded with a 4-factor interaction. In this case, you cannot tell if the calculated result is due to the main effect, due to the 4-factor interaction, or due to some combination of the two effects. Because the likelihood of the 4-factor interaction being significant is low, you assume that it does not exist. This assumption is the reason that fractional factorial experiments are statistically risky. However, the benefit of using these experiments often outweighs the risk. Experiment Designs In the past, the statistical community referred to the field of statistical problem solving as design of experiments, or DOE. This term was used because experimenters toiled over approaches to designing experiments for problem resolution. The act of designing the experiment is not an issue in die casting due to the fact that we are limited in the number of effective experimental designs available. This limitation stems from the interactive nature of die casting, as most experimental designs are for non-interactive problems. We are further limited in options for effective experimental designs because experiments with greater than five factors and greater than three levels are too large and time consuming to use. The experiment selection chart below shows the 12 choices of experiments for five or less factors and for two or three levels. To determine which experiment to use, find the experiments that have the proper number of factors. Then choose the number of levels desired and determine if confounding will be a concern.

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Experiment Selection Chart Experiment

Treatments

Type

Number of Number of Factors Levels

A B C D E F G

21 31 22 23-1 23 24-1 32

2 3 4 4 8 8 9

B vs. C B vs. C Full Factorial Taguchi F. F. Full Factorial Fractional Factorial Full Factorial

1 1 2 3 3 4 2

2 3 2 2 2 2 3

H

22x31

12

Full Factorial

3

I J

24 25-1

16 16

Full Factorial Fractional Factorial

4 5

2w/2 1w/3 4 5

K

32x21

18

Full Factorial

3

L

33

27

Full Factorial

3

2w/3 1w/2 3

Main Effects Confounded with

2 Factor Interactions Confounded with

Quality of Experiment

N/A N/A Nothing All Interactions Nothing 3 Factor Interactions Nothing

N/A N/A Nothing N/A Nothing 2 Factor Interactions Nothing

Good Good Good Bad Good Mediocre Very Good

Nothing

Nothing

Good

Nothing 4 Factor Interactions

Nothing 3 Factor Interactions

Good Very Good

Nothing

Nothing

Good

Nothing

Nothing

Good

Replications More than one casting per treatment must be collected in order to improve the power of an experiment. Choosing the appropriate number of replications will increase the likelihood that other types of random variation will not lower the confidence of the experimental results, assuming that the proper variables were initially selected for the experiment. A rough guideline for choosing the number of replications is shown below: Number of Treatments 2 to 4 2 to 4 2 to 4 8 to 12 8 to 12 8 to 12 16 to 18 16 to 18 16 to 18 > 20 > 20 > 20

Cost of Prob- Suggested Number lem per Year of Replications < $10,000 5 $10k to $100k 8 > $100k 12 < $10,000 8 $10k to $100k 12 > $100k 15 < $10,000 10 $10k to $100k 15 > $100k 20 < $10,000 15 $10k to $100k 20 > $100k 25

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8D Step 4: Determine & Verify Root Causes Conducting an Experiment To complete an experiment, your team should follow these steps: 1) Determine the experiment from the experiment selection chart. 2) Determine factor levels based upon historical data. 3) Decide how the blocks will be applied. 4) Randomize the experiment order. 5) Determine the number of replications for each treatment. 6) Determine a start time for the experiment. 7) Complete the experiment utilizing team members to: a. collect and mark castings. b. maintain and monitor blocks. c. collect process monitoring data. d. manipulate process factors. e. document all events during the experiment. 8) If necessary, process the experimental castings to the point where the defect is evident. 9) Measure the defect level using the defect ranking system. 10) Enter the casting defect results into the proper experiment spreadsheet to determine: a. the best and worst process combinations. b. the most significant process factors to control. c. the statistical confidence of your experiment. Using Spreadsheets Included with this course is on-line access that contains 12 Microsoft® Excel spreadsheets for experiment calculations and documentation. Go to diecasting.org/???? to get the course files. Directions for use and application are provided within the spreadsheet. When using a spreadsheet, always save a copy of the file first and use this copy as your working spreadsheet. Examples of the application of the spreadsheets are in chapter 12. Calculating Effects The spreadsheets noted above automatically calculate all effects for any of the experiments in the selection chart. However, if you are evaluating an experiment manually, use the following formulas:

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8D Step 4: Determine & Verify Root Causes Σ 2’s – Σ 1’s Main Effects: Effect = ------------------------------(# of Treatments/2) Σ Same – Σ Different Two-Factor Interactions: Effect = ------------------------------(# of Treatments/2) Σ Even #1’s – Σ Odd #1’s General for all effects: Effect = ----------------------------------(# of Treatments/2) For example, if you are calculating the effect for a two-factor interaction, first calculate the sum of the results of the experiment when the levels of the two factors are the same. Then subtract the sum of the results of the experiment when the levels of the two factors are different. Divide this result by one-half of the number of treatments. Determining Significance The spreadsheets noted above automatically calculate significance for any of the experiments in the selection chart. However, if you are evaluating an experiment manually follow these steps: 1) Summarize the results of all the effects. 2) Take the absolute value of each of the effects. 3) Place the effects in descending order. (The largest absolute value is the most significant effect and so on.) Determining Best and Worst Process Conditions To determine the best and worst processes, you cannot necessarily use treatment results. You must determine the best and worst processes based on the significance of the effects.

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8D Step 4: Determine & Verify Root Causes To determine the best process, follow these steps: 1) Find the effect with the highest significance. 2) If the effect is a main effect, then a positive value indicates that the best process for the factor is at level two. If negative, then the best process for the factor is at level one. 3) If the effect is a two-factor interaction, then a positive value indicates the best process for the two factors is the one in which the two factors have the same level. A negative value indicates the best process for the two factors is the one in which the two factors have different levels. 4) If the effect is an interaction of three or more factors, then a positive value indicates the best process for the factors in the interaction is one with an even number of ones. A negative value indicates the best process for the factors in the interaction is one with an odd number of ones. 5) Find the effect with the next highest significance and return to Step 2. 6) Continue Steps 2 through 4 until all factors are defined. To determine the worst process, follow these steps: 1) Find the effect with the highest significance. 2) If the effect is a main effect, then a positive value indicates that the worst process for the factor is at level one. If negative, then the worst process for the factor is at level two. 3) If the effect is a two-factor interaction, then a positive value indicates the worst process for the two factors is the one in which the two factors have different levels. A negative value indicates the worst process for the two factors is the one in which the two factors have the same level. 4) If the effect is an interaction of three or more factors, then a positive value indicates the worst process for the factors in the interaction is one with an odd number of ones. A negative value indicates the worst process for the factors in the interaction is one with an even number of ones. 5) Find the effect with the next highest significance and return to Step 2. 6) Continue Steps 2 through 4 until all factors are defined. Determining the Best and Worst Processes Effect Type Best Process Worst Process + 2 1 Main Effect 1 2 + Same Different 2 Factor Interaction Different Same + Even # of 1's Odd # of 1's General Odd # of 1's Even # of 1's

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8D Step 4: Determine & Verify Root Causes Process Optimization When defects exist, even in the best process found by using the problem solving strategies to this point, process optimization may be needed to further minimize defects. Optimization is often referred to as “response surface optimization” by statisticians. This reference roots from the way the process is graphed. For example, assume we have two interacting factors that have been proven critical to a defect. These factors are Lube Amount and Metal Temperature. We complete a two-factor, two-level experiment and find the result below:

When reviewing the graph, imagine that the casting rank is represented by height. To find the peak height of the response surface, move in the direction of highest casting rank 4 (upper left on the graph). To continue in search of the peak, we must test the three other points to the upper left.

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8D Step 4: Determine & Verify Root Causes Once we test these three process combinations, we find that the best direction to find the peak height is now to the lower left. We then test another three process combinations to the lower left. After this test we find that all points have a casting rank of 4.5. If all points are equal, then the center is likely the peak, or the optimum process. Next we test the center point of the box and find that the average casting rank is 4.75. We have now found the optimum process for these two factors, assuming that a sound problem solving process has been followed to this point. This may be the best possible process.

D) Identify Alternative Solutions Brainstorming If you are solving a special cause problem, brainstorming in the team environment is critical to finding alternative solutions once the root cause(s) has been established. In brainstorming, your team should identify multiple approaches to eliminating the root cause(s) to make sure that the best solutions are considered. Once the team has determined potential solutions, they should analyze them all and select the best solution(s) required to eliminate the root cause(s). If you are solving a chronic cause problem, defining alternative solutions consists of finding technologies and methods to maintain the best process conditions.

Determine Corrective Action Plans For both chronic and special cause problems, finding the solution(s) to the root cause(s) may require significant efforts on the part of the team and other individuals. To assure solutions are implemented in a timely and effective manner, corrective action plans should be developed and agreed upon by those with the respective responsibilities. Good corrective action plans will help the team eliminate the defect as soon as possible.

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Chapter 8 8D STEP 5: VERIFY CORRECTIVE ACTIONS Special Cause Problems To verify special cause problem resolution, we need to prove that we can turn the defect “off” and back “on” again. This test is the best verification of a solution. If the problem may not be turned off and on due to die changes or other hardware changes, ensure that the defect rate and process conditions are documented so that the effect of the solution(s) is clear.

Chronic Cause Problems To verify chronic cause problem resolution, the experiment conducted may be evaluated in one of two ways. ANOVA, which is the statistical technique taught in most design of experiments courses, does not require more testing of the process. However it is statistically flawed in most die casting situations. The second, B vs. C, does require another experiment to be conducted but is the more desirable way to confirm results. Analysis of Variance (ANOVA) ANOVA is used to evaluate the confidence in the results of a designed experiment. ANOVA is based upon the statistical F test. The F test compares two normal distributions to determine if they are significantly different from one another. It does this by comparing the magnitude of the effect of a process change to the background variation in the statistical population of data. The problem with ANOVA as it relates to die casting is that most defects such as porosity, cracks, non-fill, and casting distortion vary in a one-tailed distribution and not a normal distribution. The resulting confidence values from the ANOVA approach are then significantly lower than reality. A simplified example below will be used to explain how ANOVA works: Assume we have completed a two-factor, two-level experiment. The two most critical effects and their relative significance values are:

1 2

Effect Name Int F.T./G.V. Gate Velocity

Effect Value 1.125 -0.875

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8D Step 5: Verify Corrective Actions To complete the ANOVA, the Sum of Squares Table must first be completed. This may be done by first finding the Grand Average of the experiment data. Then by subtracting the average from each data point in the experiment and squaring the result. These results are referred to as the “difference squares.” Add up all the difference squares to find the Grand Sum of Squares. The Grand Sum of Squares Table indicates the total amount of variation that occurred in the experiment. Experiment Data Table Trial 1 Trial 2 Trial 3 Trial 4 3 2 4 3 3 2 3 2 1 2 3 1 3 3 1 3 Grand Average 2.438 Sum of Squares Table 0.316 0.191 2.441 0.316 0.316 0.191 0.316 0.191 2.066 0.191 0.316 2.066 0.316 0.316 2.066 0.316 Grand Sum of Squares 11.938 The ANOVA table may then be created by using the above data.

Effect Int F.T./G.V. Gate Velocity Residual

ANOVA Table Sum of Squares Deg. of Freedom Mean Square F-value Confidence 1.2656 1 1.2656 1.661 78.0% 0.7656 1 0.7656 1.005 66.6% 9.9063 13 0.7620

Sum of Squares for each effect = (Effect Value)2 Residual Sum of Squares = Grand Sum of Squares – Sum of Squares of all effects Degree of Freedom for each effect = 1 Degree of Freedom for Residual = (# Treatments x # Replications) – Degrees of Freedom for all effects – 1 Mean Square = Sum of Squares I Degree(s) of Freedom

F-value = Mean Square of each effect I Mean Square of Residual

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Percent Confidence* = (1 – Fdist (F-value, Degree of Freedom effect, Degree of Freedom Residual)) x 100

*Note: this is an Excel function. The Excel spreadsheet must be used to complete this calculation. The F-value is used for the F-test, which is a statistical test. The F-test compares the experimentally controlled variation to the remaining random uncontrolled variation. The more experimental control over the process, the higher the resulting confidence. The confidence column shows the confidence from the F-test. If the confidence is 95%, there is a 5% chance that the results of the experiment are due to random variation. Typically, you want to have at least a 75% confidence for each effect. If you are concerned about the confidence of your experiment, you should complete the B vs. C test below. Confirmation Run without Statistics (B vs. C Test) The B vs. C Test should be used if: 1) you do not want to calculate the confidence using ANOVA; 2) you are not comfortable with your ANOVA results; or 3) you would like to confirm your experiment results. This test compares the best process to the worst process to prove that the results of your experiment are not random.

The B vs. C Test is often more powerful than ANOVA in determining the confidence because you are directly comparing two processes rather than several processes (treatments). The B vs. C Test works well in the die casting industry because it is based on a onetailed distribution. Die casting defects always have a one-tailed distribution. Porosity, surface defects, mis-runs, heat checks, blisters, etc., are all one-tailed distributions because they cannot improve beyond perfect. The goal of this test is to show that the B, or better process, has a tighter distribution with a shorter tail than the C, or current (worse) process, that has a wider distribution with a longer tail. Die Cast Problem Solving

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8D Step 5: Verify Corrective Actions To complete a B vs. C Test, you must collect castings during the best and worst processes. You should collect three castings minimum and up to 32 castings for both the best and worst processes. To prove that the best process is truly better than the worst process, you must first arrange all of the test castings in order from best to worst. Then you must evaluate the end count of the worst process. The confidence for the confirmation run may be determined by using the following Confidence Table: Confidence 99.9%

99%

95%

90%

B vs. C Confidence Table Number of Castings Minimum End Count 14 – 16 7 18 – 28 8 30 – 62 9 >64 10 10 – 12 5 14 – 38 6 >40 7 6 3 8 – 30 4 32 – 36 5 >38 6 8 – 16 3 >18 4

If we consider the previous example used in the calculation of ANOVA, trial 3 has the worst casting results and trial 2 has the best results. Using the B versus C analysis, three out of four of the trial 3 castings are worse than all of the trial 2 castings. Experiment Data Table Trial 1 Trial 2 Trial 3 Trial 4 3 2 4 3 3 2 3 2 1 2 3 1 3 3 1 3 Therefore, since a total of eight castings are taken from trials 2 and 3 and the end count is 3, the statistical confidence is 90%. This is much higher than the confidence calculation (78%) from the ANOVA calculation.

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Die Cast Problem Solving

Chapter 9 8D STEP 6: IMPLEMENT PERMANENT CORRECTIVE ACTIONS Statistical Documentation Documentation is critical to maintaining permanent corrective actions. When completing an involved problem solving project, documenting the defect ranking system and the gains received through problem solving will enable you to verify the corrective actions at any time. If the defect problem occurs again, the best tool to re-evaluate the process is the Multi-Vari. Completing another Multi-Vari will allow you to evaluate the current status of your process and provide a foundation for further problem solving if needed.

Identify New Process Knowledge During the problem solving process, you will learn much about the process that you are studying. The previous paradigms that may have limited problem solving and this new knowledge should be investigated, communicated, and understood by those in your organization who have responsibilities related to this particular process.

Apply Lessons Learned After the new process knowledge is identified, it should be applied. This new knowledge is often the foundation for technological change within an organization. For example, if you find that die temperature control would save five percent of defects on a given part, this may justify die temperature control implementation. Most of the benefit from problem solving comes from the lessons learned about your die casting process.

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8D Step 6: Implement Permanent Corrective Actions

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Die Cast Problem Solving

Chapter 10 8D STEP 7: PREVENT RECURRENCE Long Term Verification To prove that your solution(s) is robust enough to eliminate a defect, data must be used to objectively illustrate this over time. Typically, the best way to verify defect elimination over the long term is to monitor weekly and monthly quality reports while ensuring that the procedures or technology changes are maintained on the process.

Take Advantage of Lessons Learned The resolution of a defect frequently results in lessons learned about your company’s technology and may be applied to many other processes. To fully take advantage of what you have learned through your problem solving efforts, find ways to apply this knowledge to many, or all, of your die casting processes.

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8D Step 7: Prevent Recurrence

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Chapter 11 8D STEP 8: CONGRATULATE YOUR TEAM The team that has helped resolve the defect problem by this point has exemplified the willingness to work and think above and beyond their typical responsibilities. Because your company needs to promote involvement, congratulating the team that is involved in solving a defect problem is critical. If you want problem solving efforts to be respected in your company, finding ways to promote this activity is necessary.

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8D Step 8: Congratulate Your Team

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Die Cast Problem Solving

Chapter 12 PROBLEM SOLVING EXAMPLES Problem Solving Example 1: 2-Factor, 2-Level, Full Factorial The following experiment was conducted to test the effect of die temperature and gate velocity on surface finish. The two levels determined from historical data for die temperature were 400 and 450 degrees Fahrenheit, and for gate velocity were 1400 and 1600 inches per second. The following experiment design was used: Treatment 1 2 3 4

Die Temperature (1) 400 F (2) 450 F (1) 400 F (2) 450 F

Gate Velocity (1) 1400 ips (1) 1400 ips (2) 1600 ips (2) 1600 ips

Random Order 4 2 1 3

Five castings were collected at each setting during the experiment. The castings were ranked. The results of the experiment are as follows: Treatment 1 2 3 4

D.T. (1) 400 F (2) 450 F (1) 400 F (2) 450 F

G.V. (1) 1400 ips (1) 1400 ips (2) 1600 ips (2) 1600 ips

Casting Ranks 1 2 1 2 1 2 3 2 1 2 3 2 3 2 3 1 2 1 0 1

Average 1.4 2.0 2.6 1.0

Using the two-factor, two-level spreadsheet provided, the best and worst conditions and the significance were determined. Trial 1 2 3 4 Effects Die Temp Gate Vel Int F1/F2 Best Worst

Die Temp 1 2 1 2 Value -0.5 0.1 -1.1 Die Temp 1 2

Gate Vel 1 1 2 2 0.5 0.1 1.1 Gate Vel 2 2

Results 1 1.4 1 2 2 2.6 3 1 1 Significance 2 3 1

2 2 3 2 2

3 1 2 3 1

4 2 1 2 0

1 1

2 2

-1

1

Die Cast Problem Solving

5 1 2 3 1

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Problem Solving Examples Thus, the spreadsheet shows that the best conditions are die temperature at Level 1 and gate velocity at Level 2. This result agrees with Treatment 3, where the best result was found. Also, the spreadsheet shows that the two-factor interaction between die temperature and gate velocity is the most significant effect. The main effect of die temperature is the second most significant effect.

Problem Solving Example 2: 5-Factor, 2-Level, Fractional Factorial A team at Unproductive Aluminum Inc. formed to resolve a non-fill problem on a widget assembly bracket. The team developed a zero to five ranking system for the defects. The team then conducted a Multi-Vari study and completed the TOPS Is and Is Not Questions. The clues they generated were that piece-to-piece variation and shift-to-shift variation were both significant. They knew that the defect was somewhat chronic because they always had defects at varying levels. However, from the Is and Is Not Questions, they also felt that the metal delivery and operator practices varied from shift to shift. Once the team obtained their clues, they met to determine possible causes. They determined their experimental factors to be: 1) Fast Shot Speed 2) Shot Pressure 3) Metal Temperature 4) Lube Amount 5) Cycle Time The team blocked for metal level, die temperature, and cooling water temperature. They blocked for metal level by having the metal deliveryman deliver fresh metal before each treatment. They blocked for die temperature by monitoring thermocouples in the die next to the defect, and internal water flow in local water lines. They blocked for cooling water temperature by conducting the experiment late at night when the outside cooling tower temperature was consistent and monitoring the water thermocouple in the cooling tower.

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Problem Solving Examples The experiment design was as follows: Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Fast Shot Speed Shot Pressure Metal Temperature Lube Amount Cycle Time 1 1 1 1 2 2 1 1 1 1 1 2 1 1 1 2 2 1 1 2 1 1 2 1 1 2 1 2 1 2 1 2 2 1 2 2 2 2 1 1 1 1 1 2 1 2 1 1 2 2 1 2 1 2 2 2 2 1 2 1 1 1 2 2 2 2 1 2 2 1 1 2 2 2 1 2 2 2 2 2

The team completed 16 replications for all 16 treatments. The team then ranked the casting using their defect ranking system. The results shown in the calculation spreadsheet were as follows: Replications 16 Trial Results 1 1 4.3125 4 2 2.25 2 3 4.3125 4 4 1.75 1 5 1.875 2 6 4.5625 5 7 2.3125 1 8 4.6875 5 9 1.1875 2 10 3.0625 2 11 1.625 2 12 3.75 3 13 4 4 14 1.375 1 15 3.5 3 16 1.5 0

2 4 2 4 2 2 5 2 5 2 3 1 4 5 2 3 3

3 5 3 5 2 1 4 2 4 1 4 2 4 3 1 3 2

4 5 3 4 2 2 5 2 5 1 3 1 4 4 1 4 1

5 5 2 3 3 2 4 3 4 1 2 2 5 4 1 3 2

6 4 3 4 2 1 5 2 5 2 3 2 4 4 2 3 1

7 3 2 5 3 3 4 2 5 1 4 2 3 4 2 3 1

8 4 2 4 1 2 5 3 4 0 3 1 4 4 2 3 1

9 5 2 4 2 2 4 3 5 1 3 2 4 4 1 4 1

Die Cast Problem Solving

10 11 12 13 14 15 16 5 5 4 4 4 5 3 3 3 2 2 2 1 2 5 5 4 4 5 5 4 1 2 2 2 1 1 1 2 1 2 1 2 3 2 5 4 5 4 5 4 5 1 3 4 2 2 3 2 5 4 5 5 4 5 5 2 1 1 1 2 1 0 3 4 3 2 3 3 4 2 1 1 3 1 2 1 4 2 4 5 4 2 4 5 4 3 4 5 4 3 1 1 2 2 2 1 0 3 4 3 5 5 4 3 2 1 2 2 1 2 2

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Problem Solving Examples The calculated effects and the significance from the spreadsheet were as follows: F1 F2 F3 F4 F5 Int Int Int Int Int Int Int Int Int Int

Effects Fast Shot Speed Shot Pressure Metal Temperature Lube Amount Cycle Time F1/F2 F1/F3 F1/F4 F1/F5 F2/F3 F2/F4 F2/F5 F3/F4 F3/F5 F4/F5

Value Significance -0.023 13 0.102 8 0.195 5 -0.758 2 0.070 10 0.008 14 0.133 6 -0.133 7 -0.320 3 -0.055 12 0.086 9 -2.289 1 -0.008 15 0.211 4 0.070 11

The best and worst processes tested were found to be: Best Worst

Fast Shot Speed 2 1

Shot Pressure 2 1

Metal Temperature 2 1

Lube Amount 1 2

Cycle Time 1 1

Because there are 16 other potential combinations that were not tested, we need to evaluate the significance and whether the effect is a positive or negative value to be certain that we have the actual best and worst conditions. To do this, we first look at the effect with the highest significance. This is the interaction between Factor 2 (Shot Pressure) and Factor 5 (Cycle Time). This effect is a negative value. A negative value for an interaction means that the levels for the factors in the best process must be opposite. That is, if Factor 2 has a level of one, then Factor 5 must have a level of two, or vice versa. Furthermore, this means that the levels for the factors in the worst process must be the same. Fast Shot Speed Best Best Worst Worst

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Shot Pressure 1 2 1 2

Metal Temperature

Die Cast Problem Solving

Lube Amount

Cycle Time 2 1 1 2

Problem Solving Examples The second significant effect is the main effect of Factor 4, which is Lube Amount. This effect is a negative value. A negative value for a main effect means that the level for Lube Amount in the best process must be one. Also, this means that the level for Lube Amount in the worst process must be two. Fast Shot Speed Shot Pressure Metal Temperature Lube Amount Best 1 1 Best 2 1 Worst 1 2 Worst 2 2

Cycle Time 2 1 1 2

The third significant effect is the interaction between Factor 1 (Fast Shot Speed) and Factor 5 (Cycle Time). This effect is a negative value. A negative value for an interaction means that the levels of the factors in the best process must be opposite. The worst process must be the same level. Fast Shot Speed Shot Pressure Metal Temperature Lube Amount Best 1 1 1 Best 2 2 1 Worst 1 1 2 Worst 2 2 2

Cycle Time 2 1 1 2

The fourth significant effect is the interaction between Factor 3 (Metal Temperature) and Factor 5 (Cycle Time). This effect is a positive value. A positive value for an interaction means that the levels for the factors in the best process must be the same. The levels in the worst process must be different. Fast Shot Speed Shot Pressure Metal Temperature Lube Amount Cycle Time Best 1 1 2 1 2 Best 2 2 1 1 1 Worst 1 1 2 2 1 Worst 2 2 1 2 2 The fifth significant effect is the main effect of metal temperature. The sign is positive therefore the best process must be 2 and the worst process must be 1. Fast Shot Speed Shot Pressure Best 1 1 Best 2 2 Worst 1 1 Worst 2 2

Metal Temperature 2 1 2 1

Lube Amount 1 1 2 2

Cycle Time 2 1 1 2

Or Fast Shot Speed Shot Pressure Metal Temperature Lube Amount Cycle Time Best 1 1 2 1 2 Worst 2 2 1 2 2 Die Cast Problem Solving

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Problem Solving Examples Notice that both the best and worst processes were not tested in the experiment. This shows the power of a fractional factorial design. That is, the experiment is able to accurately find the best combination of factors by using interactions without testing every combination…even if the best and worst combinations are not tested.

Problem Solving Example 3: 5-Factor, 2-Level, Fractional Factorial This problem solving exercise was completed on a lock cylinder at a die casting facility. The problem was that these automotive lock cylinders had internal porosity holes that connected with the lock tumbler spring pockets. The holes were referred to as “wormholes.” The defect would occur if the wormhole was large enough to allow the small tumbler spring to fall into it. When these tumbler springs fell into the hole, the automobile could not be started because the tumbler would fall in front of the key, which did not allow the driver to insert the key fully into the ignition. Until this problem solving exercise was completed, several engineers and outside die casting consultants had tried to resolve the problem, but were unsuccessful. The defect was costing the company several million dollars per year and was risking the relationship with the company’s second largest customer. To resolve this problem, a problem solving team was developed. The team followed the Eight Discipline format and used many of the tools that have been discussed in this book to resolve the problem. The steps taken to resolve this problem were as follows: 1. Team Approach To begin the problem solving process, the company first established a team. The team included two operators, two process engineers, one tooling engineer, one quality engineer, and the die casting manager. 2. Problem Description The team started the problem solving process by deciding upon a problem statement that was similar to the description provided above. One team member created a pictograph that was approved by the team. Then the team created a ranking system. Because the defect was a multi-million dollar per year problem and the defect was fairly easy to rank, the ranking system included 11 defect levels. The team completed a Gage Repeatability and Reproducibility study and determined that the ranking system achieved an acceptable 30% GR & R. 3. Implement and Verify Containment To ensure that defects did not get to the customer, the team implemented 100% inspection after the die casting operation and at the end of the assembly of the lock. Even with these added inspections, a few defective assemblies did make it to the customer.

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Problem Solving Examples 4. Determine and Verify Root Causes A. Identify Potential Causes (Clue Generation) In this phase the team used the TOPS Is and Is Not Questions. From these questions the team determined that this casting’s defect was unique in the plant. However, this was the only significant clue found. Using the Multi-Vari study the team found that Piece-to-Piece variation was significant. This made sense to the team because it proved the chronic nature of the defect, which is why the Is and Is Not Questions provided few clues. The Multi-Vari study showing the Piece-to-Piece, Hour-to-Hour, Shift-to-Shift, and Day-to-Day variation is shown below:

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Problem Solving Examples

B. Select Likely Causes When clue generation was completed, the next major step was to brainstorm factors for consideration in an experiment. To begin, the team reviewed the Multi-Vari data and the Is and Is Not Questions. Then the team brainstormed eight process variables (factors) that could easily vary with the time mode of variation shown in the multi-vari results. These eight factors were: 1) 2) 3) 4) 5) 6) 7) 8)

Cavity Cleanliness Cycle Time Lube Amount Metal Level Metal Temperature Nozzle Temperature Shot Pressure Shot Speed

 ight factors were listed, however, the team had to eliminate three in order to conduct E an experiment. The question that the team asked was, “Are any of these eight parameters not possible to control due to cost or lack of technology?” The answer was “yes.” Two parameters, Metal Level and Cavity Cleanliness, could not be changed in the long term because these factors were standard shop practices for many machines.  he team now had six parameters remaining. They prioritized which factor was T least important to the defect and determined that Cycle Time was least important. These three factors that are not to be used in the experiment were now to be used as blocks for the experiment.

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Die Cast Problem Solving

Problem Solving Examples C. Is the Potential Cause a Root Cause?  he experiment the team used was a five-factor, two-level, fractional factorial experiT ment. The experiment tests for main effects and two factor interactions, and ignores three, four and five factor interactions. The team conducted the experiment by manipulating the five factors and maintaining the blocks. The Metal Level was blocked filling the furnace to the same level before each treatment. Cavity Cleanliness was blocked by cleaning the cores and inserts before each treatment. Cycle Time was blocked by measuring and maintaining the cycle time for each shot during the experiment. Fifteen replications for each treatment were taken. The experiment design was as follows: Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Factor 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2

Factor 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2

Factor 3 1 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2

Factor 4 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2

Factor 5 2 1 1 2 1 2 2 1 1 2 2 1 2 1 1 2

The levels for each factor were chosen using historical data. The levels were: Trial Level 1 Level 2

Lube Amount Shot Pressure Shot Speed Nozzle Temperature Metal Temperature 0.10 sec 650 psi 5.5 ips 890 deg F 780 deg F 0.12 sec 750 psi 6.5 ips 920 deg F 800 deg F  he team completed the experiment as described above and then ranked the castT ings using their defect ranking system. The results as shown in the calculation spreadsheet were as follows:

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Problem Solving Examples

Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Results 4.47 5.07 4.40 6.33 4.73 4.60 4.60 4.67 2.67 5.40 4.87 5.07 5.40 5.47 5.20 5.87

1 2 8 5 6 4 4 3 6 2 5 3 6 4 5 5 7

2 7 1 9 2 7 1 9 2 8 1 8 2 8 1 9 2

3 7 1 0 10 0 10 0 10 2 9 2 10 0 8 1 4

4 4 5 6 5 5 3 4 4 3 3 5 5 5 3 7 6

5 8 0 10 0 8 0 10 1 10 0 10 0 10 0 10 0

6 7 0 0 10 7 4 7 2 3 8 2 8 8 10 9 9

7 0 10 1 8 1 9 1 9 0 8 1 8 2 7 2 10

8 2 8 7 5 2 4 10 9 0 6 6 4 3 10 1 7

9 2 8 7 8 8 2 10 1 0 10 6 6 10 9 0 7

10 1 9 2 7 2 6 2 7 1 6 2 7 3 6 4 9

11 5 8 0 10 8 10 1 4 0 10 2 8 10 10 9 10

12 8 5 0 2 8 2 1 7 1 5 8 2 4 0 5 4

13 5 2 7 4 6 2 7 3 6 2 6 4 7 2 8 4

14 7 10 5 8 0 2 2 1 2 8 2 6 2 1 0 9

The calculated effects and the significance from the spreadsheet were as follows: Effects Lube Amount Shot Pressure Shot Speed Nozzle Temperature Metal Temperature Int F1/F2 Int F1/F3 Int F1/F4 Int F1/F5 Int F2/F3 Int F2/F4 Int F2/F5 Int F3/F4 Int F3/F5 Int F4/F5

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Value 0.77 0.40 0.28 0.13 0.53 -0.05 -0.60 0.15 -0.05 -0.37 0.12 0.05 0.70 -0.43 0.25

Significance 1 6 8 11 4 13 3 10 14 7 12 15 2 5 9

Die Cast Problem Solving

15 2 1 7 10 5 10 2 4 2 0 10 0 5 10 8 0

Problem Solving Examples

The best and worst processes tested were found to be: Best Worst

Factor 1 2 1

Factor 2 2 1

Factor 3 1 1

Factor 4 1 2

Factor 5 2 1

 he best and worst processes tested agree with the significance shown in the sigT nificance table. This is based upon the following analysis: Significance Factor(s) Sign Best Worst 1 1 + 2 1 2 3–4 + Same Diff. 3 1–3 – Diff. Same 4 5 + 2 1 5 3–5 – Diff. Same

Agrees with Best/Worst Yes Yes Yes Yes Yes

*Since factor 2 has not yet been verified we go to #6 in significance.

6

2

+

2

1

Yes

D. Identify Alternative Solutions The experiment results showed that the following process changes should be considered: 1. T  he Lube Amount main effect is positive. Therefore, the Lube Amount should be set at level two which is 0.12 seconds. 2. The Shot Speed and Nozzle Temperature have a positive interaction. Therefore, both should be set at level two or both should be set at level one. 3. The Shot Speed and Lube Amount have a negative interaction. Therefore, since Lube Amount is at level two, then Shot Speed should be set at level one, which is 5.5 inches per second. This means that Nozzle Temperature should also be at level one, which is 890 degrees Fahrenheit. 4. The Metal Temperature main effect is positive. Therefore, Metal Temperature should be set to level two or 800 degrees Fahrenheit. 5. T  he Shot Pressure main effect is positive. Therefore, Shot Pressure should be set to level two or 750 pounds per square inch. 5. Verify Corrective Actions  lthough the best and worst processes were found, the team needed to prove that A the results were not random variation by completing a confirmation run. The team used the B vs. C test. Twenty parts were taken from the worst process and 20 parts were taken from the best process in the B vs. C test. The parts were ranked from worst to best process and the results were as shown below:

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Problem Solving Examples

End Count =8



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Worst Process Best Process 1 2 9 3 10 4 13 5 15 6 21 7 22 8 23 11 24 12 25 14 27 16 30 17 33 18 34 19 35 20 36 26 37 28 38 29 39 31 40 32

 rom the B vs. C evaluation table, the above results show a confidence of 99%. F Therefore, the experiment results were not random variation. However, some defects still exist in the best process.

Die Cast Problem Solving

Problem Solving Examples 6. Implement Permanent Corrective Actions Statistical Documentation  he Multi-Vari information from the beginning of the problem solving process T shows the original state of the process. The experiment and the B vs. C test show the current state of the process. If future process problems occur, a new Multi-Vari could be completed and compared with the experiment and old Multi-Vari results to evaluate quality and parameter settings. Identify New Process Knowledge The following process knowledge was gained from the experiment: 1. The Nozzle Temperature variation was unacceptable. 2. The experiment taught the team that the defect was not a Gas Porosity defect as had always been thought, but it was a Shrinkage Porosity defect. The team learned this because more spray would cause more gas porosity and less shrinkage. Since the defect got better with more spray then the defect must have been Shrinkage Porosity. 3. The experiment also taught the team that more spray contacting the tumbler blade causes better quality. 4. The fact that the Shot Speed needed to be lower in the best process, told the team that the velocity of metal in contact with the defect area was increasing heat in the area. Apply Lessons Learned  rom the new process knowledge gained in the experiment, the applied solutions F were as follows: 1. To set the process to the best conditions shown in the experiment. 2. To find a better way to control nozzle temperature. During the experiment the temperature varied significantly and was difficult to control to the proper level. The team found that with PID control, they could eliminate 95% of the nozzle temperature variation. 3. Now that the team knew the defect was shrinkage porosity, this indicated that the team should find a way to lighten the casting volume in the area of the shrinkage. To do this, the team spoke with the design engineers of the lock. The team found that metal savers could be placed in the area as long as the customer approved the design change. 4. To get more spray contacting the tumbler blade, the team determined that a rougher surface would hold more lubricant. Therefore, the team decided to try shot peen of the die to roughen the die surface. 5. To specifically reduce the velocity of the metal in the die without reducing fill time, the gate area must be increased. The team decided to increase the gate area and redirect the metal flow away from the defect area.

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Problem Solving Examples The results of these changes are shown in the following chart:

7. Prevent Recurrence Long Term Verification  he means of long-term verification in this problem solving example was to evaluT ate the number of defects at the assembly plant and at the customer’s site. Once the backlog of product made it through the production system, there were no defects found at the assembly plant or at the customer’s site. Take Advantage of Lessons Learned  nce this cause and effect relationship was established for wormholes, the team O found that some similar defects to wormholes existed on other parts. The knowledge of the resolution to this defect was then communicated to the persons responsible for the other parts. This resulted in several die and process design changes on other products at the facility.

Problem Solving Example 4: 3-Factor, 3-Level, Full Factorial This problem solving exercise was completed on a shower handle assembly. The handle had to be plated and therefore could not have significant surface defects. The problem was that unacceptable porosity occurred on the casting parting line. Approximately 20 percent of all products were defective. A five-factor experiment that had been completed prior to this point had shown that dwell time, hot oil temperature, and vacuum time were critical. The three-level, three-factor experiment was used to optimize the process for minimizing or eliminating the defect. The experiment design was as follows:

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Die Cast Problem Solving

Problem Solving Examples

Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Dwell Time Hot Oil Temp. Vacuum Time 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3

1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3

The levels for each factor were chosen using historical data. The levels were: Trial Level 1 Level 2 Level 3

Dwell Time Hot Oil Temp. Vacuum Time 5.00 5.75 6.50

350.00 400.00 450.00

Die Cast Problem Solving

1.50 1.75 2.00

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Problem Solving Examples The experiment was completed and the castings were ranked using the previously established defect ranking system. The results, as shown in the calculation spreadsheet, were as follows: Trial Results 1 2 3 4 5 6 7 1

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

4.321

4 4 5 5 4 4 3

4

4

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4.357

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4

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4

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4

3

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3.821

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4

4

14

3.536

1 2 3 4 5 2 3

4

5

2

3

4

5

3

4

5

3

4

4

3

4

3

4

4

4

4

3

4

15

4.250

5 4 3 2 5 4 3

5

4

3

5

4

3

5

4

3

5

4

5

4

5

4

5

5

5

5

5

5

16

3.893

2 3 4 5 2 3 4

5

2

3

4

5

3

4

5

3

4

5

4

5

4

5

4

5

4

4

4

4

17

4.107

5 4 3 5 4 3 5

4

3

5

4

3

5

4

3

5

4

5

4

5

4

4

4

4

4

4

4

4

18

4.250

3 4 5 3 4 5 3

4

5

3

4

5

4

5

4

5

4

5

4

5

4

5

4

5

4

5

4

4

19

4.000

5 4 3 5 4 3 5

4

3

5

4

3

5

4

3

5

4

3

5

4

3

5

4

3

4

4

4

4

20

3.893

3 4 5 3 4 5 3

4

5

3

4

5

3

4

5

3

4

3

4

3

4

4

4

4

4

4

4

4

21

4.107

5 4 3 2 1 5 4

3

2

5

4

5

4

5

4

5

4

5

4

5

4

5

4

5

4

5

4

5

22

3.786

2 3 4 5 2 3 4

5

3

4

5

3

4

5

3

4

5

3

4

5

3

4

3

4

4

4

4

4

23

3.857

5 4 3 2 5 4 3

4

3

4

3

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

24

3.464

1 2 3 4 5 1 2

3

4

5

1

2

3

4

5

3

4

5

3

4

5

4

4

4

4

4

4

4

25

3.679

5 4 3 2 5 4 3

2

5

4

3

4

3

4

3

4

3

4

3

4

3

4

4

4

4

4

4

4

26

3.571

1 2 3 4 5 2 3

4

5

3

5

3

4

3

4

3

4

3

4

3

4

4

4

4

4

4

4

4

27

3.750

5 4 3 5 4 3 5

4

3

5

4

3

5

4

3

4

3

4

3

4

3

4

3

4

3

4

3

3

The results of a three-level experiment may only be evaluated graphically. Graphs of casting rank versus dwell time, hot oil temperature, and vacuum time are shown as follows:

Page 70

Die Cast Problem Solving

Problem Solving Examples

The three-level experiment may not be evaluated, therefore the experiment needed to be pooled to calculate the effects. To do this, the best and worst conditions for each factor had to be determined, and all treatments where the best or worst treatments were not tested had to be eliminated. In essence, the experiment was converted from a three-factor, three-level experiment into a three-factor, two-level experiment. The pooled experiment appeared as follows:

Die Cast Problem Solving

Page 71

Problem Solving Examples

Pooled Experiment (To calculate significance and interactions) Trial Dwell Time 2 2 3 3 5 2 6 3 20 2 21 3 23 2 24 3

Hot Oil Temperature Vacuum Time 1 1 1 1 2 1 2 1 1 3 1 3 2 3 2 3

Results 4.357 4.429 4.286 3.929 3.893 4.107 3.857 3.464

From the pooled experiment we calculated the effects and determined significance: Effects Dwell Time Hot Oil Temperature Vacuum Time Int F1/F2 Int F1/F3 Int F2/F3 Int F1/F2/F3

Value -0.116 -0.313 -0.42 -0.259 0.0268 -0.027 -0.045

Significance 4 2 1 3 7 6 5

The best and worst processes were as follows (original levels in brackets): T3 Best T24 Worst

Dwell Time 2 (3) 2 (3)

Hot Oil Temperature 1 2

Vacuum Time 1 2 (3)

Using the best process, the casting defect level went from 20 percent to below two percent. Although the defect was not eliminated, the cost savings attributed to this experiment were significant.

Page 72

Die Cast Problem Solving

APPENDIX 1 Day 1 Part

Insp 1

Day 2

Insp 2 Insp 3

Avg

Rng

Part

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

Insp 1 Insp 2 Insp 3

9

9

10

10

Average

Average

Inspector 1 Avg

Grand Mean Average

Inspector 2 Avg

Grand Range Average

Inspector 3 Avg

Difference Between Evaluators Parts (n)

Maximum Part Range

Trials (r)

Evaluators (e)

Avg

Rng

Grd Avg

Appendix 1 Constants Trials (r)

K1

=

2

4.56

3

3.05

=

Eval (e)

K2

2

3.65

3

2.70

Parts (n)

K3

2

3.65

3

2.70

4

2.30

5

2.08

6

1.93

7

1.82

8

1.74

9

1.67

10

1.62

Error between evaluators (repeatability) = Grand Range Average x K1 Error within evaluators (reproducibility) =[(Diff. Bet. Eval. X K2)2 - (Repeatability2/(nxr))].5 Repeatability & Reproducibility (R&R) =[(Repeatability) + (Reproducibility) ] 2

2 .5

Part Variation (PV) = Maximum Part Range x K3

= =

Total Variation (TV) = [(R&R) + (PV) ]

=

% Repeatability = 100 x Repeatability / TV

=

2

2 .5

% Reproducibility = 100 x Reproducibility / TV % R & R = 100 x R&R / TV

= =

Die Cast Problem Solving

Page 73

Appendix 1

Page 74

Die Cast Problem Solving

APPENDIX 2 Is/Is Not Differences 1.

A. B. C. D.

2.

A. B. C. D.

3.

A. B. C. D.

4.

A. B. C. D.

5.

A. B. C. D.

6.

A. B. C. D.

7.

A. B. C. D.

8.

A. B. C. D.

Die Cast Problem Solving

Page 75

Appendix 2

Page 76

Die Cast Problem Solving

APPENDIX 3 Is/Is Not Theories T1. T2. T3. T4. T5. T6. T7. T8. T9. T10. T11. T12. T13. T14. T15.

Die Cast Problem Solving

Page 77

Appendix 3

Page 78

Die Cast Problem Solving

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