Chapter Ⅰ Histograms and Empirical Distributions 1
1.1 Introduction 1
1.2 Empirical Distributions 2
1.3 Measures of Central Tendency 7
1.4 Measures of Variation 8
1.5 Computation of the Mean and Standard Deviation from the Frequency Table 9
Chapter Ⅱ Random Variables and Probability Distributions 13
2.1 Introduction 13
2.2 Set of All Possible Outcomes of the Experiment 14
2.3 Random Variables 16
2.4 Probability and Probability Distributions 19
2.5 Discrete Probability Distributions 22
2.6 Continuous Probability Distributions 25
2.7 Random Sample 29
2.8 Expectation 30
2.9 Moments 31
2.10 Some Properties of Random Variables 35
Chapter Ⅲ The Normal Distribution 40
3.1 Definitions 40
3.2 The Mean and Variance of the Normal Distribution 41
3.2.1 Evaluation of the Mean and Variance 43
3.3 Tables of the Normal Integral 44
3.4 Combinations of Normally Distributed Variables 48
3.5 The Standardized Normal Random Variable 49
3.6 The Distribution of the Sample Mean 50
3.7 Tolerances 51
3.8 Tolerances in Complex Items 59
3.9 The Central Limit Theorem 64
Chapter Ⅳ Other Probability Distributions 70
4.1 Introduction 70
4.2 The Chi-Square Distribution 71
4.2.1 The Chi-Square Random Variable 71
4.2.2 The Addition Theorem 74
4.2.3 The Distribution of the Sample Variance 75
4.3 The t-Distribution 78
4.3.1 The t-Random Variable 78
4.3.2 The Distribution of ？ 81
4.3.3 The Distribution of the Difference Between Two Sample Means 82
4.4 The F Distribution 84
4.4.1 The F Random Variable 84
4.4.2 The Distribution of the Ratio of Two Sample Variances 86
4.5 The Binomial Distribution 87
4.5.1 The Binomial Random Variable 87
4.5.2 Tables of the Binomial Probability Distribution 89
4.5.3 The Normal Approximation to the Binomial 90
4.5.4 The Arc Sine Transformation 91
4.5.5 The Poisson Approximation to the Binomial 92
Chapter Ⅴ Significance Tests 96
5.1 Introduction 96
5.2 The Operating Characteristic Curve 98
5.3 One- and Two-Sided Procedures 103
5.4 Statistical Decision Theory 109
Chapter Ⅵ Tests of the Hypothesis about a Single Parameter 111
6.1 Tests of the Hypothesis that the Mean of a Normal Distribution Has a Specified Value when the Standard Deviation Is Known 111
6.1.1 Choice of an OC Curve 111
6.1.2 Tables and Charts for Determining Decision Rules 113
6.1.2.1 Tables and Charts for Two-Sided Procedures 113
6.1.2.2 Summary for Two-Sided Procedures 116
6.1.2.3 Tables and Charts for One-Sided Procedures 117
6.1.2.4 Summary for One-Sided Procedures 119
6.1.2.5 Tables and Charts for OC Curves 120
6.1.3 Analytical Determination of Decision Rules 122
6.1.3.1 Acceptance Regions and Sample Sizes 122
6.1.3.2 The OC Curve 125
6.1.4 Example 126
6.2 Test of the Hypothesis that the Mean of a Normal Distribution Has a Specified Value when the Standard Deviation Is Unknown 127
6.2.1 The Choice of an OC Curve 127
6.2.2 Tables and Charts for Carrying Out t Tests 129
6.2.2.1 Tables and Charts for Two-Sided Procedures 130
6.2.2.2 Summary for Two Sided Procedures 131
6.2.2.3 Tables and Charts for One-Sided Procedures 131
6.2.2.4 Summary for One-Sided Procedures 134
6.2.2.5 Tables and Charts for OC Curves 134
6.2.3 Examples of t Tests 136
6.3 Test of the Hypothesis that the Standard Deviation of a Normal Distribution Has a Specified Value 137
6.3.1 Choice of an OC Curve 137
6.3.2 Charts and Tables to Design Tests of Dispersion 138
6.3.2.1 Tables and Charts for Two-Sided Procedures 138
6.3.2.2 Summary for Two-Sided Procedure Using Tables and Charts 140
6.3.2.3 Tables and Charts for One-Sided Procedures 140
6.3.2.4 Summary for One-Sided Procedures Using Tables and Charts 143
6.3.2.5 Tables and Charts for Operating Character-istic Curves 144
6.3.3 Analytical Treatment for Chi-Square Tests 145
6.3.4 Example 147
Chapter Ⅶ Tests of Hypotheses about Two Parameters 156
7.1 Test of the Hypothesis that the Means of Two Normal Distribu-tions Are Equal when Both Standard Deviations Are Known 156
7.1.1 Choice of an OC Curve 156
7.1.2 Tables and Charts for Determining Decision Rules 157
7.1.2.1 Tables and Charts for Two-Sided Procedures 157
7.1.2.2 Summary for Two-Sided Procedures Using Tables and Charts 159
7.1.2.3 Summary for One-Sided Procedures Using Tables and Charts 159
7.1.2.4 Tables and Charts for Operating Character-istic Curves 161
7.1.3 Analytical Determination of Decision Rules 162
7.1.3.1 Acceptance Regions and Sample Sizes 162
7.1.3.2 The Operating Characteristic Curve 164
7.1.4 Example 165
7.2 Test of the Hypothesis that the Means of Two Normal Distribu-tions Are Equal Assuming that the Standard Deviations Are Unknown but Equal 166
7.2.1 Choice of an OC Curve 166
7.2.2 Tables and Charts for Carrying out Two Sample t Tests 167
7.2.2.1 Tables and Charts for Two-Sided Procedures 168
7.2.2.2 Summary for Two-Sided Procedures Using Tables and Charts 169
7.2.2.3 Summary for One-Sided Procedures Using Tables and Charts 169
7.2.2.4 Tables and Charts for Operating Character-istic Curves 170
7.2.3 Example 172
7.3 Test of the Hypothesis that the Means of Two Normal Distribu-tions Are Equal Assuming that the Standard Deviations Are Unknown and not Necessarily Equal 173
7.3.1 Test Procedure 173
7.3.2 Example 174
7.4 Test for Equality of Means when the Observations Are Paired 175
7.4.1 Test Procedure 175
7.4.2 Example 178
7.5 Non-parametric Tests 179
7.5.1 The Sign Test 179
7.5.2 The Wilcoxon Signed Rank Test 179
7.5.3 A Test for Two Independent Samples 184
7.6 Test of the Hypothesis that the Standard Deviations of Two Normal Distributions Are Equal 186
7.6.1 Choice of an OC Curve 186
7.6.2 Charts and Tables for Carrying out F Tests 187
7.6.2.1 Tables and Charts for Two-Sided Procedures 187
7.6.2.2 Summary for Two-Sided Procedures Using Tables and Charts 189
7.6.2.3 Tables and Charts for One-Sided Procedures 189
7.6.2.4 Summary for One-Sided Procedures Using Tables and Charts 191
7.6.2.5 Tables and Charts for Operating Character-istic Curves 192
7.6.3 Analytical Treatment for Tests 193
7.6.4 Example 195
7.7 Cochran’s Test for the Homogeneity of Variances 198
Chapter Ⅷ Estimation 211
8.1 Introduction 211
8.2 Point Estimation 211
8.3 Optimal Estimates 214
8.4 Confidence Interval Estimation 215
8.5 Confidence Interval for the Mean of a Normal Distribution when the Standard Deviation Is Known 216
8.5.1 Example 217
8.6 Confidence Interval For the Mean of a Normal Distribution when the Standard Deviation Is Unknown 217
8.6.1 Example 218
8.7 Confidence Interval for the Standard Deviation of a Normal Distribution 219
8.7.1 Example 219
8.8 Confidence Interval for the Differen between the Means of Two Normal Distributions when the Standard Deviations Are Both Known 220
8.8.1 Example 221
8.9 Confidence Interval for the Difference between the Means of Two Normal Distributions where the Standard Deviations Are Both Unknown but Equal 221
8.9.1 Example 222
8.10 Confidence Interval for the Ratio of Standard Deviations of Two Normal Distributions 223
8.10.1 Example 224
8.11 A Table of Point Estimates and Interval Estimates 224
8.12 Statistical Tolerance Limits 224
8.12.1 Example 228
8.13 One-Sided Statistical Tolerance Limits 229
8.13.1 Example 229
8.14 Distribution-Free Tolerance Limits 229
Chapter Ⅸ Fitting Straight Lines 238
9.1 Introduction 238
9.2 Types of Linear Relationships 242
9.3 Least Squares Estimates of the Slope and Intercept 243
9.3.1 Formulation of the Problem and Results 243
9.3.2 Theory 245
9.4 Confidence Interval Estimates of the Slope and Intercept 246
9.4.1 Formulation of the Problem and Results 246
9.4.2 Theory 248
9.5 Point Estimates and Confidence Interval Estimates of the Average Value of y for a Given x 249
9.5.1 Formulation of the Problem and Results 249
9.5.2 Theory 250
9.6 Point Estimates and Interval Estimates of the Independent Variable x Associated with an Observation on the Dependent Variable y 251
9.7 Prediction Interval for a Future Observation on the Dependent Variable 253
9.7.1 Formulation of the Problem and Results 253
9.7.2 Theory 254
9.8 Tests of Hypotheses about the Slope and Intercept 255
9.9 Estimation of the Slope B when A is Known to be Zero 257
9.10 Ascertaining Linearity 259
9.11 Transforming to a Straight Line 261
9.12 Work Sheets for Fitting Straight Lines 264
9.13 Illustrative Examples 264
9.14 Correlation 273
Chapter Ⅹ Analysis of Variance 286
10.1 Introduction 286
10.2 Model for the One-Way Classification 287
10.2.1 Fixed Effects Model 287
10.2.2 Random Effects Model 289
10.2.3 Further Examples of Fixed Effects and of the Random Effects Models 290
10.2.4 Computational Procedure: One-Way Classification 290
10.2.5 The Analysis of Varian Procedu 292
10.2.5.1 A Heuristic Justification 292
10.2.5.2 The Partition Theorem 293
10.2.6 Analysis of the Fixed Effects Model: One-Way Clas-sification 294
10.2.7 The OC Curve of the Analysis of Variance for the Fixed Effects Model 299
10.2.8 Example Using the Fixed Effects Model 305
10.2.9 Analysis of the Random Effects Model 307
10.2.10 The OC Curve for the Random Effects Model 307
10.2.11 Example Using the Random Effects Model 313
10.2.12 Randomization Tests in the Analysis of Variance 314
10.3 Two-Way Analysis of Variance， One Observation per Combina-tion 315
10.3.1 Fixed Effects Model 316
10.3.2 Random Effects Model 319
10.3.3 Mixed Fixed Effects and Random Effects Model 319
10.3.4 Computational Procedure， Two-Way Classification， One Observation per Combination 320
10.3.5 Analysis of the Fixed Effects Model， Two-Way Classification， One Observation per Combination 321
10.3.6 The OC Curve of the Analysis of Variance for the Fixed Effects Model: Two-Way Classification， One Observation per Combination 324
10.3.7 Example Using the Fixed Effects Model 325
10.3.8 Analysis of the Random Effects Model: Two-Way Classification， One Observation per Combination 327
10.3.9 The OC Curve for the Random Effects Model: Two-Way Classification 328
10.3.10 Example Using the Random Effects Model 329
10.3.11 Analysis of the Mixed Effects Model， Two-Way Classification， One Observation per Combination 330
10.3.12 The OC Curve of the Analysis of Variance for the Mixed Effects Model， Two-Way Classification， One Observation per Cell 331
10.3.13 Example Using the Mixed Effects Model 332
10.4 Two-Way Analysis of Variance， n Observations per Combination 332
10.4.1 Description of the Various Models 332
10.4.2 Computational Procedure， Two-Way Classification， n Observations per Cell 334
10.4.3 Analysis of the Fixed Effects Model， Two-WayClassification， n Observations per Combination 335
10.4.4 The OC Curve of the Analysis of Variance for the Fixed Effects Model， Two-Way Classification， n Observations per Cell 339
10.4.5 Example Using the Fixed Effects Model， Two-Way Classification， Three Observations per Combination 340
10.4.6 Analysis of the Random Effects Model， Two-Way Classification， n Observations per Combination 342
10.4.7 The OC Curve of the Random Effects Model， Two-Way Classification， n Observations per Combination 344
10.4.8 Example Using the Random Effects Model 345
10.4.9 Analysis of the Mixed Effects Model， Two-Way Classification， n Observations per Cell 345
10.4.10 The OC Curve of the Analysis of Variance for the Mixed Effects Model， Two-Way Classification， One Observation per Cell 347
10.4.11 Example Using the Mixed Effects Model 347
10.5 Summary of Models and Tests 349
Chapter ⅩⅠ Analysis of Enumeration Data 365
11.1 Enumeration Data 365
11.2 Chi-Square Tests 365
11.3 The Hypothesis Completely Specifies the Theoretical Frequency 366
11.3.1 Dichotomous Data 367
11.4 Test of Independence in a Two-Way Table 369
11.4.1 Computing Form for Test of Independence in a 2 by 2 Table 370
11.5 Comparison of Two Percentages 371
11.6 Confidence Intervals for Proportion 372
11.6.1 Exact Confidence Intervals for p 373
11.6.2 Normal Approximations to Confidence Intervals 373
Chapter ⅩⅡ Statistical Quality Control: Control Charts 378
12.1 Introduction 378
12.2 Obtaining Data From Rational Subgroups 378
12.3 Control Chart for Variables: ? - Charts 379
12.3.1 Statistical Concepts 379
12.3.2 Estimates of ?’ 381
12.3.3 Estimate of ?’ by ? 381
12.3.4 Estimate of ?’ by ? 383
12.3.5 Starting a Control Chart for ? 383
12.3.6 Relation Between Natural Tolerance Limits and Specification Limits 384
12.3.7 Interpretation of Control Charts for ? 385
12.4 R Charts and ? Charts 387
12.4.1 Statistical Concepts 387
12.4.2 Setting up a control chart for R or ? 388
12.5 Example of ? and R Chart 389
12.6 Control Chart For Fraction Defective 391
12.6.1 Relation Between Control Charts Based on Variables Data and Charts Based on Attributes Data 391
12.6.2 Statistical Theory 391
12.6.3 Starting the Control Chart 393
12.6.4 Continuing the p Chart 394
12.6.5 Example 395
12.7 Control Charts For Defects 395
12.7.1 Difference Between a Defect and a Defective 395
12.7.2 Statistical Theory 396
12.7.3 Starting and Continuing the c Chart 396
12.7.4 Example 396
Chapter ⅩⅢ Sampling lnspection 402
13.1 The Problem of Sampling Inspection 402
13.1.1 Introduction 402
13.1.2 Drawing the Sample 403
13.2 Lot-by-Lot Sampling Inspection by Attributes 404
13.2.1 Single Sampling Plans 404
13.2.1.1 Single Sampling 404
13.2.1.2 Choosing a Sampling Plan 406
13.2.1.3 Calculation of OC Curves for Single Sampling Plans 407
13.2.1.4 Example 407
13.2.2 Double Sampling Plans 413
13.2.2.1 Double Sampling 413
13.2.2.2 OC Curves for Double Sampling Plans 413
13.2.2.3 Example 414
13.2.3 Multiple Sampling Plans 415
13.2.4 Classification of Sampling Plans 416
13.2.4.1 Classification By AQL 416
13.2.4.2 Classification By LTPD 416
13.2.4.3 Classification By Point of Control 416
13.2.4.4 Classification By AOQL 417
13.2.5 Dodge-Romig Tables 418
13.2.5.1 Single Sampling Lot Tolerance Tables 418
13.2.5.2 Double Sampling Lot Tolerance Tables 421
13.2.5.3 Single Sampling AOQL Tables 421
13.2.5.4 Double Sampling AOQL Tables 421
13.2.6 Military Standard 105A 424
13.2.6.1 History 424
13.2.6.2 Classification of Defects 425
13.2.6.3 Acceptable Quality Levels 425
13.2.6.4 Normal， Tightened， and Reduced Inspection 426
13.2.6.5 Sampling Plans 427
13.2.7 Designing your Own Attribute Plan 432
13.2.7.1 Computing the OC Curve of a Single Sampling Plan 457
13.2.7.2 Finding a Sampling Plan Whose OC Curve Passes Through Two Points 457
13.2.7.3 Design of Item by Item Sequential Plans 464
13.3 Lot-By-Lot Sampling Inspection By Variables 467
13.3.1 Introduction 467
13.3.2 General Inspection Criteria 468
13.3.3 Estimates of the Percent Defective 470
13.3.3.1 Estimate of the Percent Defective when the Standard Deviation Is Unknown but Estimated by the Sample Standard Deviation 470
13.3.3.2 Estimate of the Percent Defective when the Standard Deviation Is Unknown but Estimated by the Average Range 471
13.3.3.3 Estimate of the Percent Defective when the Standard Deviation Is Known 489
13.3.4 Comparison of Variables Procedures with M and k 491
13.3.5 The Military Standard for Inspection by Variables，MIL-STD-414 492
13.3.5.1 Introduction 492
13.3.5.2 Section A— General Description of Sampling Plans 493
13.3.5.3 Section B — Variability Unknown，Standard Deviation Method 494
13.3.5.4 Section C — Variability Unknown， Range Method 510
13.3.5.5 Section D — Variability Known 511
13.3.5.6 Example Using MIL-STD-414 512
13.4 Continuous Sampling Inspection 513
13.4.1 Introduction 513
13.4.2 Dodge Continuous Sampling Plans 513
13.4.3 Multi-Level Sampling Plans 537
13.4.4 The Dodge CSP-1 Plan without Control 541
13.4.5 Wald-Wolfowitz Continuous Sampling Plans 542
13.4.6 Girshick Continuous Sampling Plan 543
13.4.7 Plans Which Provide for Termination of Production 544
Appendix 553
lndex 569