WAYNE NELSON

Con tents
1. Overview and Background
1. Introduction, 1
2. Overview of the Book, 3
3. Background Material, 5
2. Basic Concepts and Distributions for Product Life
1
15
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10.
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12.
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15.
General Theory on Continuous Distributions (Illustrated
by the Exponential Distribution), 16
Normal Distribution, 28
Lognormal Distribution, 32
Weibull Distribution, 36
Smallest Extreme Value Distribution, 39
Gamma and Chi-square Distributions, 44
Other Distributions, 47
Shifted Distributions, 54
Conditional and Truncated Distributions. 56
Joint Distributions and the Joint Normal
Distribution. 7 1
General Theory on Discrete Distributions (Geometric
Distribution), 78
Poisson Distribution, 84
Binomial Distribution, 9 I
Hypergeometric Distribution. 96
Multinomial Distribution. 98
Problems. 100
3. Probability Plotting of Complete and Singly Censored Data 103
How to Make a Probability Plot of Complete Data, 108
1 . Motivation, 104
2.
3. Percentiles and Probabilities, 110
4.
5 .
6.
7.
8.
9.
10.
1 1 .
CONTENTS
Exponential Probability Plot. 110
Normal Probability Plot, 1 1 1
Lognormal Probability Plot, 113
Weibull Probability Plot, 1 15
Extreme Value Probability Plot, 116
Aids for Data Plotting, 117
Probability Plots of Singly Censored Data, 120
Theory for Probability Papers, 125
Problems, 128
4. Graphical Analysis of Multiply Censored Data
1. Hazard Plotting, 132
2.
3.
Probability Plotting of Multiply Censored Data, 146
Theory for Hazard Papers, 154
Problems, 158
5. Series Systems and Competing Risks
1.
2.
3.
Series Systems of Different Components, 163
Series Systems of Identical Parts, 168
Hazard Plots for Data with Competing Failure
Modes, 173
Problems, 187
6. Analysis of Complete Data
1.
2. Poisson Data. 200
3. Binomial Data, 204
4. Exponential Data, 20Y
5. Normal and Lognormal Data, 216
6. Weibull and Extreme Value Data, 226
7. Distribution-Free Methods, 235
Problems, 243
Basic Ideas for Data Analysis, 194
7. Linear Methods for Singly Censored Data
1. Basic Concepts, 248
2. Exponential Data, 251
3.
4.
5. Order Statistics, 294
Normal and Lognormal Data, 261
Weibull and Extreme Value Data, 276
Problems, 309
8. Maximum Likelihood Analysis of Multiply Censored Data
Introduction, 3 13
1. Exponential Distribution, 316
2. Normal and Lognormal Distributions, 323
3. Weibull and Extreme Value Distributions, 333
4. Data with Competing Failure Modes- Maximum
Likelihood Analysis, 347
5. General Maximum Likelihood Methods and Theory, 356
6. Numerical Methods, 386
Problems, 395
siii
313
9. Analyses of Inspection Data (Quantal-Response and Interval Data) 405
Introduction, 405
I . Graphical Analyses of Quantal-Response Data, 407
2. Maximum Likelihood Fitting for Quantal-Response
Data, 41 1
3. Graphical Analyses of Interval Data, 414
4. Maximum Likelihood Analyses for Interval Data. 418
5. ML Theory for Interval and Quantal-Response Data. 421
Problems. 427
10. Comparisons (Hypothesis Tests) for Complete Data
Introduction, 433
1. Comparison of Poisson Samples, 438
2. Comparison of Binomial Samples, 447
3. Comparison of Multinomial Samples, 453
4. Comparison of Exponential Samples, 459
5. Comparison of Normal and Lognormal Samples, 469
6. Nonparametric, Weibull, and Other Distributions, 490
7. Theoretical Concepts for Hypothesis Tests, 491
Problems, 494
11. Comparisons With Linear Estimators (Singly Censored and
Complete Data)
1. One-Sample Comparisons, 505
2.
3. Two-Sample Comparisons. 510
4. K-Sample Comparisons, 5 15
Pooled Estimate of a Common Parameter Value, 509
12. Maximum Likelihood Comparisons (Multiply Censored and
Other Data) 522
1. One-Sample Comparisons, 523
2.
3. Two-Sample Comparisons, 527
4. K-Sample Comparisons, 53 1
5. Likelihood Ratio Tests, 534
6.
Pooled Estimate of a Common Parameter Value, 525
General Theory for Likelihood Ratio and Related
Tests, 539
Problems, 553
13. Survey of Other Topics 558
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System Reliability Models and Their Analyses, 559
Maintainability Models and Data Analyses, 56 1
Availability Models and Data Analyses, 562
Estimation of System Reliability From Component
Data, 562
Bayesian Methods in Reliability, 562
Reliability Demonstration and Acceptance Tests, 563
Reliability Growth (Duane Plots), 564
Renewal Theory and Data Analysis, 564
Life as a Function of Other Variables. 565
Accelerated Life Testing, 566
Depreciation, Replacement. and Maintenance
Policies, 566
Books on Reliability and Life Data Analysis, 567
Abstracts, Bibliographies, and Indices on Reliability
and Life Data Analysis, 569
Journals with Papers on Reliability and Life Data
Analysis. 570
Computerized Literature Searches, 57 1
Problems. 572