Acceptance Sampling in Quality Control, Third Edition | Edward G. Schilling and Dean V. Neubauer

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Acceptance Sampling in Quality Control, Third Edition
By Edward G. Schilling and Dean V. Neubauer

Acceptance Sampling

Contents
Preface to the Third Edition………………………………………………………………xix
Note from the Series Editor for the First Edition…………………………….xxi
Foreword to the First Edition………………………………………………………… xxiii
Preface to the First Edition…………………………………………………………….xxv
Acknowledgments from the First Edition……………………………………… xxvii
Preface to the Second Edition……………………………………………………….xxix
Authors……………………………………………………………………………………………xxxi
List of Tables…………………………………………………………………………………….. xxxiii
1. Introduction…………………………………………………………………………1
Acceptance Quality Control……………………………………………………1
Acceptance Control and Process Control……………………………………………..4
Process Quality Control……………………………………………………………………..4
Background of Acceptance Quality Control………………………………………..7
Top 10 Reasons for Acceptance Sampling…………………………………9
Problems……………………………………………………………………………………………10
References…………………………………………………………………………………..10
2. Probability and the Operating Characteristic Curve………….13
Probability…………………………………………………………………………………..13
Classical Definition………………………………………………………………………………………………13
Empirical Definition…………………………………………………………………………………………….13
Subjective Definition…………………………………………………………………………………………….14
Random Samples and Random Numbers…………………………………………………………………14
Counting Possibilities……………………………………………………………………………………………….15
Probability Calculus…………………………………………………………………………………………………19
Operating Characteristic Curve………………………………………………………………………………..23
Software Applications………………………………………………………………………………………………27
Excel …………………………………………………………………………………………………………………….27
Minitab…………………………………………………………………………………………………………………29
Problems…………………………………………………………………………………………………………………..32
References………………………………………………………………………………………………………………..33
3. Probability Functions………………………………………………………………………………………………35
Probability Distributions………………………………………………………………………………………….36
Measures of Distribution Functions………………………………………………………………………….39
Hypergeometric Distribution……………………………………………………………………………………41
Binomial Distribution……………………………………………………………………………………………….43
Poisson Distribution…………………………………………………………………………………………………45
f-Binomial Distribution…………………………………………………………………………………………….49
Negative Binomial Distribution………………………………………………………………………………..51
Exponential and Continuous Distributions………………………………………………………………53
Weibull Distribution…………………………………………………………………………………………………55
Normal Distribution…………………………………………………………………………………………………57
Summary of Distributions………………………………………………………………………………………..60
Tables of Distributions……………………………………………………………………………………………..60
Hypergeometric Tables………………………………………………………………………………………..60
Binomial Tables……………………………………………………………………………………………………63
Poisson Tables………………………………………………………………………………………………………64
Negative Binomial Tables…………………………………………………………………………………….64
Exponential and Weibull Tables……………………………………………………………………………65
Normal Distribution Tables………………………………………………………………………………….65
Summary………………………………………………………………………………………..65
Useful Approximations…………………………………………………………………………………………….66
Tests of Fit………………………………………………………………………………………………………………..69
Software Applications……………………………………………………………………………72
Excel ……………………………………………………………………………………………….72
Minitab…………………………………………………………………………………………………74
Problems………………………………………………………………………………………..79
References……………………………………………………………………………………………80
4. Concepts and Terminology……………………………………………………………………………………..83
Average Run Length of Type B Plans………………………………………………………………………..86
Sample Size and Lot Size………………………………………………………………………………………….87
Effect of Inspection Error………………………………………………………………………………………….90
Rectification……………………………………………………………………………………………………………..92
Curtailment………………………………………………………………………………………………………………94
Tolerance and Confidence Intervals………………………………………………………………………….97
Levels and Risks……………………………………………………………………………………………………….99
Choosing Quality Levels…………………………………………………………………………………………101
Classification of Defects………………………………………………………………………………………….102
Measures of Sampling Plans: Terminology……………………………………………………………..102
Graphs of Measures………………………………………………………………………………………………..104
Specifying a Plan…………………………………………………………………………………………………….107
Software Applications…………………………………………………………………………………………….108
Minitab……………………………………………………………………………………………………………….108
Problems……………………………………………………………………………………………….. 110
References………………………………………………………………………………………… 111
5. Single Sampling by Attributes…………………………………………………………………………….. 113
Operation………………………………………………………………………………………………………………. 113
Selection………………………………………………………………………………………………………………… 113
Tables of Poisson Unity Values………………………………………………………………………….. 114
Binomial Nomograph………………………………………………………………………………………… 116
f-Binomial Nomograph……………………………………………………………………………………… 116
Thorndyke Chart……………………………………………………………………………………………….. 118
Hypergeometric Tables……………………………………………………………………………………… 119
Measures………………………………………………………………………………………………………………..121
Software Applications…………………………………………………………………………………………….123
Excel………………………………………………………………………………………………123
Minitab……………………………………………………………………………………………………………….125
Statgraphics………………………………………………………………………………………………………..127
Problems…………………………………………………………………………………………………………………130
References………………………………………………………………………………………………………………131
6. Double and Multiple Sampling by Attributes……………………………………………………..133
Operation……………………………………………………………………………………………………………….134
Double Sampling………………………………………………………………………………………………..134
Multiple Sampling……………………………………………………………………………………………..134
Selection…………………………………………………………………………………………………………………135
Measures………………………………………………………………………………………………………………..141
Double Sampling………………………………………………………………………………………………..141
Multiple Sampling……………………………………………………………………………………………..143
Further Considerations…………………………………………………………………………………………..151
Software Applications…………………………………………………………………………………………….151
Excel…………………………………………………………………………………………151
Minitab……………………………………………………………………………………………………………….154
Statgraphics………………………………………………………………………………………………………..154
Problems…………………………………………………………………………………………………………………156
References………………………………………………………………………………………………………………157
7. Sequential Sampling by Attributes………………………………………………………………………159
Operation……………………………………………………………………………………………………………….159
Selection…………………………………………………………………………………………………………………161
Measures………………………………………………………………………………………………………………..163
Sequential Sampling for Defects per Unit……………………………………………………………….165
Software Applications…………………………………………………………………………………………….166
Excel…………………………………………………………………………………………………………………..166
Problems…………………………………………………………………………………………………………………170
References………………………………………………………………………………………………………………171
8. Variables Sampling for Process Parameter……………………………………………………………173
Single Sampling for Process Parameter…………………………………………………………………..173
Acceptance Control Charts……………………………………………………………………………………..175
Sequential Plans for Process Parameter (σ Known)…………………………………………………179
Sequential Plans for Process Parameter (σ Unknown)…………………………………………….187
Cumulative Sum Charts………………………………………………………………………………………….190
Problems…………………………………………………………………………………………………………………193
References………………………………………………………………………………………………………………194
9. Bulk Sampling……………………………………………………………………………………………………….195
Construction of the Sample…………………………………………………………………………………….196
Estimation………………………………………………………………………………………………………………198
Sampling Plans……………………………………………………………………………………………………….207
Simple Random Sampling of a Unique Lot (Components of Variance Unknown)….209
Sampling from Stream of Lots………………………………………………………………………………..212
Estimation of Testing and Reduction Variances………………………………………………….212
Estimation of Segment and Increment Variances………………………………………………..213
Application of Plan to Stream of Lots…………………………………………………………………214
ISO 10725………………………………………………………………………………………………………………..216
Problems…………………………………………………………………………………………………………………218
References………………………………………………………………………………………………………………219
10. Sampling by Variables for Proportion Nonconforming……………………………………….221
Specification Limits………………………………………………………………………………………………..222
Assumptions and Theory……………………………………………………………………………………….223
Operation……………………………………………………………………………………………………………….225
X Method…………………………………………………………………………………………………………..225
k Method…………………………………………………………………………………………………………….225
Double Specification Limits………………………………………………………………………………..226
Selection…………………………………………………………………………………………………………………231
Tables…………………………………………………………………………………………………………………231
Formulas…………………………………………………………………………………………………………….232
Jacobson Nomograph for Plan Selection…………………………………………………………….233
Measures………………………………………………………………………………………………………………..234
Jacobson Nomograph for Operating Characteristics…………………………………………..234
Calculation: σ Known…………………………………………………………………………………………235
Calculation: σ Unknown…………………………………………………………………………………….236
Double Specification Limits………………………………………………………………………………..240
Measures of Performance…………………………………………………………………………………..242
M Method……………………………………………………………………………………………………………….243
Plans Based on Sample Range………………………………………………………………………………..248
Example……………………………………………………………………………………………………………..250
Double Sampling by Variables………………………………………………………………………………..252
Tolerance Intervals and Variables Plans for Percent Nonconforming……………………..255
Sequential Plans for Proportion Nonconforming……………………………………………………259
Further Considerations…………………………………………………………………………………………..260
Derivation of n, k Formulas………………………………………………………………………………..260
Need for Normality……………………………………………………………………………………………262
Software Applications…………………………………………………………………………………………….262
Minitab……………………………………………………………………………………………………………….262
Statgraphics………………………………………………………………………………………………………..269
Problems…………………………………………………………………………………………………………………273
References………………………………………………………………………………………………………………274
11. Attributes Sampling Schemes……………………………………………………………………………….277
Sampling Schemes………………………………………………………………………………………………….277
Quick Switching Systems……………………………………………………………………………………….277
Tightened–Normal–Tightened Plans………………………………………………………………………279
MIL-STD-105E and Derivative Standards……………………………………………………………….279
Operation……………………………………………………………………………………………………………….281
Selection…………………………………………………………………………………………………………………283
Measures………………………………………………………………………………………………………………..286
Scheme Properties…………………………………………………………………………………………………..287
Implementation of MIL-STD-105E………………………………………………………………………….289
Matching Individual Sampling Plans to MIL-STD-105E System Performance………..294
MIL-STD-105 Derivatives……………………………………………………………………………………….296
ANSI/ASQ Standard Z1.4………………………………………………………………………………….297
ASTM International Standard E2234…………………………………………………………………..297
ISO Standard 2859………………………………………………………………………………………………297
Further Considerations…………………………………………………………………………………………..299
Software Applications…………………………………………………………………………………………….300
Minitab……………………………………………………………………………………………………………….300
Snap Sampling Plans!…………………………………………………………………………………………300
Statgraphics………………………………………………………………………………………………………..301
Problems…………………………………………………………………………………………………………………306
References………………………………………………………………………………………………………………307
12. Variables Sampling Schemes………………………………………………………………………………..309
MIL-STD-414………………………………………………………………………………………………………….309
Operation………………………………………………………………………………………………………………. 311
Selection…………………………………………………………………………………………………………………313
Measures………………………………………………………………………………………………………………..316
Implementation of Form 2………………………………………………………………………………………317
Implementation of Form 1………………………………………………………………………………………319
Implementation of Plans for Range and Variability Known……………………………………320
Match between MIL-STD-414 and MIL-STD-105E………………………………………………….320
Conversion of MIL-STD-414 to ANSI/ASQ Z1.9…………………………………………………….321
MIL-STD-414 Derivatives……………………………………………………………………………………….322
ANSI/ASQ Z1.9…………………………………………………………………………………………………322
ASTM International Standard E2762…………………………………………………………………..322
ISO 3951-1…………………………………………………………………………………………………………..323
Further Considerations…………………………………………………………………………………………..326
Software Applications…………………………………………………………………………………………….326
Excel…………………………………………………………………………………………………………………..326
Minitab……………………………………………………………………………………………………………….327
Statgraphics………………………………………………………………………………………………………..327
Problems…………………………………………………………………………………………………………………334
References………………………………………………………………………………………………………………335
13. Special Plans and Procedures………………………………………………………………………………..337
No-Calc Plans…………………………………………………………………………………………………………337
Lot Plot Plans………………………………………………………………………………………………………….339
Narrow-Limit Gauging…………………………………………………………………………………………..344
Mixed Variables: Attributes Plan…………………………………………………………………………….354
Advantages and Disadvantages of Mixed Plans…………………………………………………356
Generalized Mixed Dependent Procedure………………………………………………………….357
Measures: Independent Mixed Plan……………………………………………………………………358
Measures: Dependent Mixed Plan………………………………………………………………………360
MIL-STD-414 Dependent Mixed Plans……………………………………………………………….365
Comparison of Independent and Dependent Mixed Plans…………………………………366
Comparison of Mixed with Other Type Plans…………………………………………………….367
Problems…………………………………………………………………………………………………………………368
References………………………………………………………………………………………………………………369
14. Series of Lots: Rectification Schemes…………………………………………………………………….371
Single-Sampling AOQL Plan…………………………………………………………………………………..372
Dodge–Romig Sampling Scheme……………………………………………………………………………373
Operation…………………………………………………………………………………………………………..374
Selection……………………………………………………………………………………………………………..374
Measures…………………………………………………………………………………………………………….381
Further Considerations………………………………………………………………………………………381
Constructing LTPD Plan with Minimum ATI…………………………………………………386
Constructing AOQL Plan with Minimum ATI………………………………………………..388
Anscombe Rectifying Inspection Procedure……………………………………………………………391
Operation…………………………………………………………………………………………………………..391
Selection……………………………………………………………………………………………………………..392
Measures…………………………………………………………………………………………………………….394
Credit-Based Schemes…………………………………………………………………………………………….395
Dodge–Romig Plan Derivatives……………………………………………………………………………..398
Software Applications…………………………………………………………………………………………….398
Excel…………………………………………………………………………………………………………………..398
Snap Sampling Plans!…………………………………………………………………………………………405
Problems…………………………………………………………………………………………………………………407
References………………………………………………………………………………………………………………407
15. Continuous Sampling Plans………………………………………………………………………………….409
Dodge Continuous Plans………………………………………………………………………………………..409
Dodge CSP-1………………………………………………………………………………………………………409
Dodge–Torrey CSP-2 and CSP-3…………………………………………………………………………412
Measures of CSP-1, 2, and 3………………………………………………………………………………..415
Stopping Rules and Selection of CSP-1 Plans……………………………………………………..420
Multilevel Plans……………………………………………………………………………………………………..423
Tightened Multilevel Plans……………………………………………………………………………………..427
Block Continuous Plans………………………………………………………………………………………….428
Wald–Wolfowitz Plan…………………………………………………………………………………………428
Girshick Plan………………………………………………………………………………………………………430
MIL-STD-1235B………………………………………………………………………………………………………431
MIL-STD-1235B Derivatives……………………………………………………………………………………439
ASTM International Standard E2819…………………………………………………………………..439
Software Applications…………………………………………………………………………………………….439
Excel…………………………………………………………………………………………………………………..439
Snap Sampling Plans!…………………………………………………………………………………………442
Problems…………………………………………………………………………………………………………………443
References………………………………………………………………………………………………………………444
16. Cumulative Results Plans……………………………………………………………………………………..445
Skip-Lot Sampling Plans…………………………………………………………………………………………445
SkSP-1………………………………………………………………………………………………………………..445
SkSP-2………………………………………………………………………………………………………………..447
Chain Sampling Plans…………………………………………………………………………………………….453
ChSP-1……………………………………………………………………………………………………………….453
Two-Stage Plans…………………………………………………………………………………………………457
Deferred Sentencing Schemes…………………………………………………………………………………458
Demerit Rating Plan……………………………………………………………………………………………….462
CRC Plan………………………………………………………………………………………………………………..466
Software Applications…………………………………………………………………………………………….468
Excel…………………………………………………………………………………………………………………..468
Problems…………………………………………………………………………………………………………………474
References………………………………………………………………………………………………………………475
17. Compliance Sampling……………………………………………………………………………………………477
LSP…………………………………………………………………………………………………………………………478
Procedure…………………………………………………………………………………………………………..478
Protection…………………………………………………………………………………………………………..479
Producer’s Risk………………………………………………………………………………………………….481
Examples of LSP Applications……………………………………………………………………………482
Further Considerations………………………………………………………………………………………484
TNT Scheme……………………………………………………………………………………………………………484
Procedure…………………………………………………………………………………………………………..485
Protection…………………………………………………………………………………………………………..485
Selection……………………………………………………………………………………………………………..487
Quick Switching System…………………………………………………………………………………………489
MIL-STD-1916………………………………………………………………………………………………………..494
Structure…………………………………………………………………………………………………………….494
Operation…………………………………………………………………………………………………………..494
Implementation………………………………………………………………………………………………….496
Measures…………………………………………………………………………………………………………….498
Further Considerations………………………………………………………………………………………498
Simplified Grand Lot Procedure……………………………………………………………………………..499
Simon’s Approach………………………………………………………………………………………………500
Simplified Procedure: Attributes………………………………………………………………………..502
Example: Attributes……………………………………………………………………………………………503
Simplified Procedure: Variables………………………………………………………………………….504
Continuing Series of Lots……………………………………………………………………………………510
Further Considerations………………………………………………………………………………………513
Nomograph for Samples Having Zero Defectives…………………………………………………..515
Accept on Zero Plans………………………………………………………………………………………………515
U.S. Department of Defense Approach……………………………………………………………….515
Squeglia Plans…………………………………………………………………………………………………….516
AoZ and AQL Plans……………………………………………………………………………………………517
Chain Sampling Alternative……………………………………………………………………………….519
The Zero Acceptance Number Chained Quick Switching System………………………521
Summary……………………………………………………………………………………………………………524
Software Applications…………………………………………………………………………………………….525
Excel…………………………………………………………………………………………………………………..525
LSP Plans……………………………………………………………………………………………………….525
TNT Plans………………………………………………………………………………………………………525
QSS Plans……………………………………………………………………………………………………….527
MIL-STD-1916 Plans………………………………………………………………………………………537
Chain Sampling Alternative Plans………………………………………………………………….538
Zero Acceptance Number Chained Quick Switching System Plans……………….538
Minitab……………………………………………………………………………………………………………….543
Snap Sampling Plans!…………………………………………………………………………………………544
LSP Plans……………………………………………………………………………………………………….544
Squeglia Plans………………………………………………………………………………………………..545
Statgraphics………………………………………………………………………………………………………..545
MIL-STD-1916 Plans………………………………………………………………………………………545
Problems…………………………………………………………………………………………………………………547
References………………………………………………………………………………………………………………548
18. Reliability Sampling……………………………………………………………………………………………..551
Censored Sampling…………………………………………………………………………………………………552
Variables Plans for Life Testing and Reliability (Juran 1999)……………………………………554
Handbook H-108…………………………………………………………………………………………………….555
Operation…………………………………………………………………………………………………………..556
Failure Terminated…………………………………………………………………………………………558
Time Terminated…………………………………………………………………………………………….558
Sequential………………………………………………………………………………………………………558
Proportion Failing by Specified Time……………………………………………………………..558
Selection…………………………………………………………………………………………………………558
Example of H-108 Application……………………………………………………………………………561
Failure Terminated…………………………………………………………………………………………561
Time Terminated…………………………………………………………………………………………….561
Sequential………………………………………………………………………………………………………563
Proportion of Lot Failing by Specified Time…………………………………………………..563
Measures………………………………………………………………………………………………………..564
Further Considerations………………………………………………………………………………………564
Technical Report TR7………………………………………………………………………………………………565
Mean Life Criterion…………………………………………………………………………………………….566
Hazard Rate Criterion………………………………………………………………………………………..568
Reliable Life Criterion………………………………………………………………………………………..568
TR7 Tables………………………………………………………………………………………………………….568
Operation…………………………………………………………………………………………………………..569
TR7 with the MIL-STD-105E System…………………………………………………………………..576
Further Considerations………………………………………………………………………………………576
Problems…………………………………………………………………………………………………………………578
References………………………………………………………………………………………………………………579
19. Administration of Acceptance Sampling………………………………………………………………581
Selection and Implementation of a Sampling Procedure…………………………………………583
Determining Quality Levels……………………………………………………………………………………586
Setting AQL………………………………………………………………………………………………………..587
Setting AOQL……………………………………………………………………………………………………..590
Setting IQ……………………………………………………………………………………………………………590
Setting LTPD (or LQ)………………………………………………………………………………………….590
Relation of Levels……………………………………………………………………………………………….591
Setting PQL and CQL…………………………………………………………………………………………593
Economic Considerations……………………………………………………………………………………….593
Mandatory Standards……………………………………………………………………………………………..595
Basic Principle of Administration……………………………………………………………………………596
Problems…………………………………………………………………………………………………………………596
References………………………………………………………………………………………………………………597
Answers to Problems……………………………………………………………………………………………………599
Appendix 615
Index829

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