182186281-previews-AIAG-SPC-3-pre-pdf.pdf

Statistical Process Control

SPC Second Edition

 STA  STATISTICAL PROCESS  PROCESS  CONTROL

(SPC)

REFERENCE MANUAL

Copyright © 1992, 1992, © 1995, © 2005 2005 Daimler Chrysler Corporation, Ford Motor Company, and General Motors Corporation ISBN# 978-1-60534-108-8

TABLE OF CONTENTS CHAPTER I ................. .................. .................. .................. .................. ................. ................... .................. . 1

Continual Improvement and Statistical Process Control......................... Control....... .................. .................. ................... ........... 1  Introduction ................. ................. .................. ................. .................. ................. ................... ................ 3 Six Points .................. .................. ................. .................. ................. .................. ................... ................. . 4 CHAPTER I – Section A .................. ........................... .................. .................. .................. .................. .................. .................. .................. .................. ................. ................. .................7 ........7

Prevention Versus Detection ................. .................. ................. .................. ................. ..................... ......... 7 CHAPTER I – Section B .................. ........................... .................. .................. .................. .................. .................. .................. .................. .................. ................. ................. .................9 ........9

A Process Control System................... System. .................. .................. .................. .................. .................. ................. ............. 9 CHAPTER I – Section C .................. ........................... .................. .................. .................. .................. .................. .................. .................. .................. ................. ................. ............... ...... 13

Variation: Common.................................................................................................................................13 and Special Causes ................ .................. .................. .................. .................. .................. ................... ..... 13 CHAPTER I – Section D .................. ........................... .................. .................. .................. .................. .................. .................. .................. .................. ................. ................. ............... ...... 17

Local Actions And Actions On The System .................. .................. .................. .................. ................... 17 CHAPTER I – Section E .................. ........................... .................. .................. .................. .................. .................. .................. .................. .................. ................. ................. ............... ...... 19

Process Control and Process Capability ................... .................. .................. ................... ................... ..... 19 Control vs. Capability..................... .................. ................. .................. .................. ................... ........... 19  Process Indices ................ .................. .................. .................. .................. .................. .................. ........ 21 CHAPTER I – Section F............ .................. .................. .................. .................. .................. ................... .. 25

The Process Process Improvement Improvement Cycle and Process Process Control............. Control............................... .................. .................. .................. ......... 25 CHAPTER I – Section G ................. .................. .................. .................. .................. ................... .............. 29

Control Charts: Tools For Process Control and Improvement.................. Improvement .................. ................... .................. ........ 29  How do they work? ................ .................. .................. .................. .................. .................. .................. .. 30  Approach: ................. .................. .................. ................. .................. ................. .................. ................. 32 CHAPTER I – Section H ................. .................. .................. .................. .................. ................... .............. 37

Effective Use and Benefits of Control Charts ................ ................... .................. ................... ................. 37 CHAPTER II ................ .................. .................. .................. .................. .................. .................. ................. 41

Control Charts ................ .................. ................. .................. ................. .................. ................... .............. 41  Introduction:.... .................. ................. .................. .................. ................. .................. .................. ........ 43 Variables Control Charts .................. .................. .................. .................. .................. .................. ........ 45  Attributes Control Charts Charts .................. .................. .................. .................. .................. .................. ........ 47   Elements of Control Charts Charts .................. .................. .................. .................. .................. .................. ..... 48 CHAPTER II - Section A ................. .......................... .................. .................. .................. .................. .................. .................. .................. .................. ................... ................... ............. .... 53

Control Chart Process.............. .................. ................. .................. .................. .................. .................. ..... 53  Preparatory Steps .................. .................. .................. .................. .................. .................. ................. ... 53 Control Chart Mechanics .................. .................. .................. .................. .................. .................. ........ 55 Establish Control Limits ................ .................. .................. .................. .................. .................. ........ 59 Interpret for Statistical Control ................... .................. ................... .................. .................. ............ 60 Final Comments .................. .................. .................. .................. .................. .................. ................. .. 63 Extend Control Limits for Ongoing Control.................. Control .................. .................. .................. .................. ............ 65 CHAPTER II - Section B .................. .................. .................. .................. .................. ................. .............. 69

Defining “Out-of-Control” Signals .................. .................. .................. .................. .................. ............... 69  Point Beyond a Control Limit... Limit..................... .................. .................. .................. .................. .................. ................. 69  Patterns or Trends Within Within the Control Limits .................. .................. ................... .................. ............ 70 Special Cause Criteria............. .................. .................. .................. .................. .................. .................. 75  Average Run Length (ARL)................... ................. .................. ................. .................. .................... ..... 76  CHAPTER II - Section C ................. .......................... .................. .................. .................. .................. .................. .................. .................. .................. ................... ................... ............. .... 79

Control Chart Formulas.......................... Formulas........ .................. .................. .................. .................. .................. ................. ........ 79

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Variables Control Charts .................. .................. .................. .................. .................. .................. ........ 79 Average and Range Charts

( X , R ) 

.............................................................................................79

Average and Standard Deviation Charts Median and Range Charts

( X , R  )

( X , s ) 

...........................................................................83

.................................................................................................85

Individuals and Moving Range Charts

( X , MR ) 

........................................................................87

 Attributes Control Charts Charts .................. .................. .................. .................. .................. .................. ........ 89 Control Charts for Nonconforming Items ................. .................. .................. ................. .................. 89 Proportion Nonconforming ( p ( p   Chart)...............................................................................................89  Number of Nonconforming Chart Chart (np ( np   Chart) ..................................................................................93  Number of Nonconformities Nonconformities per Unit Chart (u ( u  Chart).....................................................................95  Number of Nonconformities Nonconformities Chart (c ( c Chart) Chart) .................. ........................... .................. .................. ................... ................... .................. .................. ........... 97 CHAPTER III .................. ........................... .................. .................. .................. .................. .................. .................. .................. .................. .................. ................. .................. ................... ............. .... 99

Other Types of Control Charts ................ .................. .................. .................. .................. ................... ..... 99  Introduction ................. ................. .................. ................. .................. ................. ................... ............ 101  Probability Based Charts Charts ......................... .................. .................. .................. .................. ................. 101 Short-Run Control Charts..................... .................. .................. .................. .................. .................. ... 107  Charts for Detecting Small Changes ................ .................. .................. .................. .................. ......... 109  Non-Normal Charts ................ .................. .................. .................. .................. .................. ................. 113  Multivariate ................ .................. .................. .................. ................. .................. .................. ............ 116  Other Charts .................. .................. .................. .................. .................. .................. ................. ......... 117  Regression Control Charts ................ .................. .................. .................. .................. .................. ... 117 Residual Charts ................ .................. .................. .................. .................. .................. ................. ... 118 Autoregressive Charts ................. .................. ................. .................. .................. ................. ........... 118 Zone Charts....................................................................................................................................121 CHAPTER IV............. .................. .................. .................. .................. .................. ................. ................. . 125

Understanding Process Capability....................... .................. .................. ................... .................. ......... 125 and Process Performance for Variables Data ................. .................. ................... .................. ................ 125  Introduction ................. ................. .................. ................. .................. ................. ................... ............ 127  CHAPTER IV - Section A ................. .................. .................. .................. .................. ................. ............ 131

Definitions of Process Terms .................. .................. .................. ................... .................. .................. ... 131 Process Measures for Predictable Predictable Processes Processes ................... .................. ................... .................. ............... 132  Indices – Bilateral Tolerances.............. .................. .................. ................... .................. .................. . 132  Indices – Unilateral Tolerances .................. .................. ................... .................. ................... ........... 137  CHAPTER IV - Section B .................. ........................... .................. .................. .................. .................. .................. .................. .................. .................. .................. .................. ........... 139

Description of Conditions .................. .................. .................. .................. .................. .................. ......... 139 Handling Non-Normal and and Multivariate Multivariate Distributions Distributions ................. .................. .................. .................. .. 140  Relationship of Indices Indices and Proportion Nonconforming.................. .................. ................. .............. 140  Non-Normal Distributions Distributions Using Transformations.... Transformations...................... .................. .................. .................. ................. 140  Non-Normal Distributions Distributions Using Non-Normal Non-Normal Forms................. Forms ................. ................... .................. ................ 142  Multivariate Distributions Distributions ................ .................. .................. .................. .................. ................... ...... 144 CHAPTER IV - Section C ................. .................. .................. .................. .................. ................. ............ 147

Suggested Use of Process Measures .................. .................. ................... .................. .................. .......... 147 The Loss Function Concept ................. .................. .................. .................. .................. ................... ... 148  Alignment of Process Process to Customer Requirements............. Requirements............. .................. .................. .................. ........... 153 APPENDIX A ................. ................. .................. ................. .................. ................. ................... ............... 157

Some Comments on Sampling ................ .................. .................. .................. .................. ................... ... 157  Effects of Subgrouping........... Subgrouping............................ ................. .................. .................. .................. .................. .................. . 157 

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 Autocorrelated Data ................. .................. .................. .................. .................. .................. ............... 157   Multiple Stream Process Process Example..................... Example.. ................... .................. .................. ................... .................. ....... 162  Effects of Sample Size on Indices.............. ................... .................. .................. ................... ............... 168 APPENDIX B .................. ........................... .................. .................. .................. ................... ................... .................. .................. .................. .................. ................. .................. ................... ........... .. 171

Some Comments on Special Causes ................. .................. ................... .................. ................... .......... 171 Over-Adjustment................................................................................................................................171 Time Dependent Processes ................ .................. .................. .................. .................. .................. ...... 173  Repeating Patterns............................... .................. .................. ................. .................. .................... ... 175 APPENDIX C ................. ................. .................. ................. .................. ................. ................... ............... 177

Selection Procedure for for the Use of the the Control Charts Described in This This Manual.................... Manual.. .................. ........... 177 APPENDIX D ................. ................. .................. ................. .................. ................. ................... ............... 179

Relationship Between C pm and Other Indices ................ .................. .................. .................. ................. 179 APPENDIX E .................. ........................... .................. .................. .................. ................... ................... .................. .................. .................. .................. ................. .................. ................... ........... .. 181

Table of Constants and Formulas Formulas for Control Charts........... ................... .................. ................... ......... 181 APPENDIX F ................. ................. .................. ................. .................. ................. ................... ............... 185

Capability Index Calculations Example ................. .................. .................. ................... .................. ...... 185 Data Set: .................. .................. .................. .................. .................. .................. .................. ................. . 186 Analysis.................................................................................................................................................187  Diameter Statistics: Statistics: ..................... .................. .................. .................. .................. .................. ............ 188 Conclusion:........................................................................................................................................190 APPENDIX G................... G.. ................. .................. .................. ................. .................. ................. ................... ............ 191

Glossary of Terms and Symbols .................. .................. ................... .................. ................... ............... 191 Terms Used in This Manual................. .................. .................. .................. .................. ................... ... 191 Symbols as Used in This Manual........................... Manual......... .................. .................. .................. .................. .................. ... 204 APPENDIX H................... H.. ................. .................. .................. ................. .................. ................. ................... ............ 211

References and Suggested Readings ................. .................. ................... .................. ................... .......... 211 APPENDIX I ................. ........................... ................... .................. .................. .................. .................. .................. .................. .................. ................... .................. ................. ................... ............. ... 215

Standard Normal Tables................... Tables.. ................. .................. .................. .................. .................. .................... ......... 215 INDEX...................... INDEX.... .................. .................. .................. .................. .................. .................. ................. ................. .... 217 S.P.C. Manual User Feedback Process .................. .................. ................... .................. ................... ..... 221

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LIST OF ILLUSTRATIONS Figure I.1: A Process Control System.......... .................. ................... .................. .................. ................. ....... 8 Figure I.2: Variation: Common Cause and Special Cause....................... ................... .................. .............. 12 Figure I.3: Process Process Control and Process Capability........... ................... .................. ................... ................. 18 Figure I.4: The The Process Improvement Cycle .................. .................. .................. ................... ................... .. 24 Figure I.5: Control Charts ................. .................. .................. .................. .................. ................. ................. 28 Figure II.1: Variables Data ................. .................. .................. .................. .................. .................. .............. 44 Figure II.2: Attributes Data.................... Data.. .................. ................... .................. ................... .................. ................ ........... 46 Figure II.3: Elements of Control Charts.................... .................. ................. .................. .................. ........... 49 Figure II.4a: Sample Control Chart (Front side)................... side) ................... .................. ................... .................. .............. 51 Figure II.4b: Sample Control Control Chart (back side) – Event Log .................. .................. .................. ............... 52 Figure II.5: Extending Control Limits ................. .................. .................. .................. .................. ............... 56 Figure II.6: Control Limits Recalculation..... ................... .................. .................. ................... .................. .. 61 Figure II.7: Extend Control Control Limits Limits for Ongoing Control............... .................. .................. .................. ....... 64 Figure II.8: Process Variation Relative to to Specification Specification Limits Limits ................ ................... .................. ............ 67 Figure II.9: Points Points Beyond Control Limits ................. .................. .................. .................. .................. ........ 70 Figure II.10: Runs in an Average Average Control Control Chart........................ Chart...... .................. ................... .................. ................... ......... 71 Figure II.11: Runs in a Range Range Control Chart ................ .................. .................. .................. ................... ..... 72 Figure II.12: Nonrandom Patterns in a Control Chart.................. .................. .................. .................. ......... 74 Figure II.13: Average and Range Charts ................ ................... .................. .................. ................... .......... 78 Figure II.14: Average and Standard Deviation Charts...................... Charts.... .................. ................... .................. ................... .. 82 Figure II.15: Median and Range Charts..................... Charts... .................. .................. .................. .................. ................... ........ 84 Figure II.16: Individual and Moving Range Charts .................. .................. .................. .................. ............ 86 Figure II.17: Proportion Nonconforming Chart ................. ................. .................. ................. ................... .. 88 Figure II.18: Number of Nonconforming Chart............... .................. .................. .................. ................ ..... 92 Figure II.19: Number of Nonconforming per Unit Chart .............................. .................. .................. ......... 94 Figure II.20: Number of Nonconformities Chart .................. .................. ................... .................. ............... 96 Figure III.1: Control Charts ................. .................. .................. .................. .................. ................. ............ 100 Figure III.2: Stoplight Control ................ .................. ................... .................. ................... ........................ ............... ......... 102 Figure III.3: Pre-Control ................ .................. .................. .................. .................. ................. ................. . 105 Figure III.4: DNOM Control Chart....................... Chart..... .................. ................... .................. ................... ................ ............ 108 Figure III.5: CUSUM Chart with V-Mask....................... V-Mask..... .................. .................. ................... .................. .................. 109 Figure III.6: X, III.6: X, MR  MR  Chart..........................................................................................................................110 Figure III.7: EWMA Chart of Viscosity .................. .................. ................... .................. ................. ......... 112 Figure III.8: X, III.8: X, MR Chart of Viscosity......................... .................. .................. .................. .................. .... 112 Figure IV.1: Within- and Between-Subgroup Variation......... .................. ................. .................. ............. 130 Figure IV.2: C  pk and P  and P  pk  Comparison................ Comparison ................ ................. .................. ................. .................. .................. 133 Figure IV.3: Comparison between between a Predictable Predictable and Immature Process................. Process ................. ................... .............. 135 Figure IV.4: Cpk  and Ppk   and Ppk  Values   Values Produced by a Predictable and Immature Process ................... ........... 136 Figure IV.5: “Goal Post” Post” vs. Loss Function Function ................. .................. ................... .................. .................. ... 148 Figure IV.6: Comparison of Loss Function Function and Specifications.................... Specifications.. .................. ................... .................. ....... 150 Figure IV.7: Comparison of Loss Functions.................. .................. .................. .................. .................. ... 151 Figure IV.8: A Process Control System...................... System.... .................. .................. ................... .................. ................. ...... 152 Figure IV.9: Process Alignment to Requirements ................. .................. .................. ................... ............ 154

 

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