Preface	8
	Section and Equation Numbering and Referencing	13
	Contents	14
	Part I Distribution Theory and Models	23
	Chapter1 Progressive Censoring: Data and Models	24
	1.1 Progressively Censored Data	25
	1.1.1 Progressive Type-II Censoring	26
	General Progressive Type-II Censoring	31
	1.1.2 Progressive Type-I Censoring	31
	Progressive Type-I Interval Censoring	35
	1.1.3 Progressive Hybrid Censoring	35
	Type-I Progressive Hybrid Censoring	36
	Type-II Progressive Hybrid Censoring	38
	1.2 Probabilistic Models in Progressive Censoring	40
	Chapter2 Progressive Type-II Censoring: Distribution Theory	42
	2.1 Joint Distribution	42
	2.2 Connection to Generalized Order Statistics and Sequential Order Statistics	45
	2.3 Results for Particular Population Distributions	47
	2.3.1 Exponential Distributions	47
	2.3.2 Reflected Power Distribution and UniformDistribution	52
	2.3.3 Pareto Distributions	54
	2.3.4 Progressive Withdrawal and Dual Generalized Order Statistics	54
	2.4 Marginal Distributions	56
	2.4.1 Exponential Distribution	57
	2.4.2 Uniform Distribution	59
	2.4.3 General Distributions	59
	Multiply Censored Progressively Type-II Censored Order Statistics	61
	An Important Recurrence Relation	62
	An Alternative Approach to Derive the Marginals	63
	Connection of Marginals to Interpolation Polynomials	64
	2.5 Conditional Distributions	65
	2.5.1 Markov Property	65
	2.5.2 Distributions of Generalized Spacings	67
	2.5.3 Block Independence of Progressively Type-II Censored Order Statistics	68
	2.5.4 Dependence Structure of Progressively Type-II Censored Order Statistics	72
	2.6 Basic Recurrence Relations	74
	2.7 Shape of Density Functions	76
	2.7.1 Log-Concavity of Uniform Progressively Type-II Censored Order Statistics	77
	2.7.2 The Shape of Densities of Uniform Progressively Type-II Censored Order Statistics	78
	2.7.3 Unimodality and Log-Concavity of Progressively Type-II Censored Order Statistics Based on F	80
	2.8 Discrete Progressively Type-II Censored Order Statistics	82
	2.9 Exceedances	86
	Chapter3 Further Distributional Results on Progressive Type-II Censoring	88
	3.1 Characterizations by Progressively Type-II Censored Order Statistics	88
	3.1.1 Characterizations by Independence Properties	88
	3.1.2 Characterizations by Distributional Properties	90
	3.1.3 Characterizations via Regression	91
	Conditional Expectations and Characterization Problems	92
	Adjacent Progressively Type-II Censored Order Statistics	93
	Progressively Type-II Censored Order Statistics Based on Higher-Order Gap	97
	Reversed Regression of Adjacent Progressively Type-II Censored Order Statistics	98
	3.1.4 Characterizations for Discrete Parents	99
	Characterization by Regression	100
	Characterization by Distribution Properties	101
	Characterization by (Conditional) Independence	102
	3.2 Stochastic Ordering of Progressively Type-II Censored Order Statistics	103
	3.2.1 Univariate Stochastic Orders and Its Applications to Progressively Type-II Censored Order Statistics	103
	Stochastic Order	103
	Hazard Rate Order	105
	Likelihood Ratio Order	106
	Dispersive Order	109
	Minimal Bounds w.r.t. Stochastic, Hazard, and Likelihood Ratio Order	111
	Lorenz Order and Convex Orders	111
	3.2.2 Multivariate Stochastic Orderings and Its Applications to Progressively Type-II Censored Order Statistics	113
	Stochastic Order	113
	Likelihood Ratio Order	113
	3.2.3 Applications to Spacings of Progressively Type-II Censored Order Statistics	116
	3.3 Aging Properties	118
	3.4 Asymptotic and Extreme Value Results	119
	3.4.1 Extreme Value Analysis for Order Statistics	119
	3.4.2 Extreme Value Analysis for Progressively Type-II Censored Order Statistics	120
	3.4.3 Extreme Value Analysis for Exponential Progressively Type-II Censored order statistics	123
	3.4.4 Extreme Value Analysis for Progressively Type-II Censored Order Statistics from a Cumulative Distribution Function F	124
	Positive Asymptotic Variance	124
	Zero Asymptotic Variance	125
	3.4.5 Applications to Upper, Lower, Central, and Intermediate Progressively Type-II Censored Order Statistics	127
	Upper Progressively Type-II Censored Order Statistics	128
	Lower Progressively Type-II Censored Order Statistics	128
	Central and Intermediate Progressively Type-II Censored Order Statistics	129
	3.4.6 Limits for Central Progressively Type-II Censored Order Statistics with Blocked Observations	130
	3.5 Near Minimum Progressively Type-II CensoredOrder Statistics	133
	Chapter4 Progressive Type-I Censoring: Basic Properties	135
	4.1 Distribution and Block Independence	135
	4.2 Number of Observations	142
	Chapter5 Progressive Hybrid Censoring: Distributions and Properties	145
	5.1 Type-I Progressive Hybrid Censoring	145
	5.1.1 Spacings for Exponential Distribution	147
	5.1.2 Distributions of Total Time on Test and Related Statistics	150
	5.1.3 Moment Generating Function	152
	5.2 Type-II Progressive Hybrid Censoring	156
	5.2.1 Exponential Distributions	157
	5.3 Generalized Progressive Hybrid Censoring	160
	Generalized Progressive Type-I Hybrid Censoring	161
	Generalized Progressive Type-II Hybrid Censoring	161
	Chapter6 Adaptive Progressive Type-II Censoring and Related Models	163
	6.1 General Model of Adaptive Progressive Type-II Censoring	164
	Distributional Assumptions	165
	6.2 Particular Models	170
	6.2.1 Nonadaptive Type-II Progressive Censoring	170
	6.2.2 Ng–Kundu–Chan Model	170
	6.2.3 Flexible Progressive Censoring	171
	6.2.4 Progressive Censoring with Random Removals	172
	Chapter7 Moments of Progressively Type-II Censored Order Statistics	174
	7.1 General Distributions	174
	7.1.1 Representations for Moments	174
	7.1.2 Existence of Moments	175
	7.2 Moments for Particular Distributions	180
	7.2.1 Exponential Distribution	180
	7.2.2 Weibull Distributions	181
	7.2.3 Reflected Power Distribution	182
	7.2.4 Uniform Distribution	183
	7.2.5 Pareto Distribution	184
	7.2.6 Lomax Distribution	185
	7.2.7 Extreme Value Distribution	185
	7.3 Recurrence Relations for Moments	186
	7.3.1 General Results	186
	7.3.2 Results for Particular Distributions	186
	Exponential Distribution	187
	Truncated Exponential Distribution	189
	Truncated Pareto Distributions	191
	Truncated Power Distributions	193
	Truncated Reflected Power Distributions	194
	Logistic and Related Distributions	196
	Doubly Truncated Burr Distributions	197
	7.4 Moments for Symmetric Distributions	198
	7.5 Bounds for Moments	201
	7.5.1 Bounds Based on the Cauchy–Schwarz Inequality	201
	7.5.2 Bound Based on the Method of Greatest Convex Minorant	203
	7.5.3 Further Bounds	206
	7.6 First-Order Approximations to Moments	209
	Chapter8 Simulation of Progressively Censored Order Statistics	211
	8.1 Generation of Progressively Type-II Censored Order Statistics	211
	8.1.1 Generation of General Progressively Type-II Censored Order Statistics	214
	8.1.2 Generation of Progressively Type-II Censored Order Statistics from a One-Step Censoring Plan	215
	8.1.3 Simulation of Progressively Hybrid Censored Data	215
	8.2 Progressively Type-I Censored Data	216
	8.3 Progressively Type-I Interval Censored Data	217
	Chapter9 Information Measures	219
	9.1 Fisher Information in Progressively Type-II CensoredSamples	219
	9.1.1 Hazard Rate Representation of Fisher Information	219
	Fisher Information in Location or Scale Family	221
	Fisher Information in the Multiparameter Case	222
	9.1.2 Fisher Information via Missing Information Principle	224
	9.1.3 Fisher Information for Particular Distributions	227
	Invariance of Fisher Information Under Progressive Censoring	227
	Weibull Distribution (Shape) and Extreme Value Distribution (Scale)	227
	Laplace Distribution (Location)	229
	Logistic Distribution	229
	Normal Distribution	230
	Lomax Distribution	230
	9.1.4 Recurrence Relations for Fisher Information	230
	9.2 Fisher Information in Progressive Hybrid Censoring	232
	9.3 Tukey's Linear Sensitivity Measure	233
	9.4 Entropy	234
	9.5 Kullback–Leibler Information	239
	9.6 Pitman Closeness	242
	Chapter10 Progressive Type-II Censoring Under Nonstandard Conditions	247
	10.1 Mixture Representation for Progressively Type-II Censored Order Statistics with Arbitrary Distribution	247
	10.2 Joint Density Function of Progressively Type-II Censored Order Statistics	249
	Modeling of Outliers	252
	Connection to Permanents	253
	Applications to Stochastic Orderings	254
	10.3 Dependence Structure of INID Progressively Type-II Censored Order Statistics	257
	10.4 Dependence and Copulas	259
	10.5 Progressive Type-II Censoring for Multivariate Observations	261
	Part II Inference	263
	Chapter11 Linear Estimation in Progressive Type-II Censoring	264
	11.1 Preliminaries	264
	11.1.1 Least-Squares Estimation	265
	11.1.2 Linear Equivariant Estimation	267
	11.1.3 First-Order Approximations to BLUEs and BLEEs	268
	11.2 Linear Estimation for Particular Distributions	269
	11.2.1 Exponential Distributions	269
	Linear Estimates	270
	11.2.2 Generalized Pareto Distributions	272
	Uniform Distribution	276
	Pareto Distribution	277
	Lomax Distribution	279
	11.2.3 Weibull and Extreme Value Distributions	279
	11.2.4 Laplace Distribution	280
	11.2.5 Logistic Distributions	282
	11.3 Asymptotic Best Linear Unbiased Estimatorsfor Blocked Progressively Type-II Censored Order Statistics	282
	Chapter12 Maximum Likelihood Estimation in Progressive Type-IICensoring	284
	12.1 Exponential Distribution	285
	Scale Parameter Unknown	285
	Location Parameter Unknown	287
	Location and Scale Parameters Unknown	287
	12.2 Weibull Distribution	291
	12.3 Reflected Power Distribution	294
	Shape Parameter Known	294
	Shape Parameter Unknown	296
	12.4 Uniform Distribution	297
	Location Parameter ? Known	297
	Location Parameter ? Unknown	298
	12.5 Pareto Distributions	298
	Shape Parameter Unknown, Scale Parameter Known	299
	Shape Parameter Known, Scale Parameter Unknown	300
	Shape and Scale Parameter Unknown	301
	Shape and Scale Parameter Unknown with Equal Location Scale	302
	12.6 Laplace Distribution	303
	Location Parameter ?R Known and Scale Parameter >0 Unknown	304
	Location Parameter ?R Unknown and Scale Parameter >0 Known	306
	Location Parameter ?R and Scale Parameter >0 Unknown	310
	12.7 Some Other Location–Scale Families	312
	12.7.1 Weibull Distributions	313
	12.7.2 Normal Distributions	314
	12.7.3 Log-Normal Distributions	316
	12.7.4 Extreme Value Distribution (Type I)	317
	12.7.5 Logistic Distribution	317
	12.8 Other Distributions	318
	12.9 Related Methods	320
	12.9.1 Modified Maximum Likelihood Estimation	321
	12.9.2 Approximate Maximum Likelihood Estimation	322
	Extreme Value Distribution	322
	Weibull Distribution	323
	Other Distributions	324
	12.10 M-Estimation	325
	12.11 Order Restricted Inference	327
	Chapter13 Point Estimation in Progressive Type-I Censoring	330
	13.1 Exponential Distribution	331
	13.1.1 One-Parameter Exponential Distribution	331
	13.1.2 Two-Parameter Exponential Distribution	334
	13.1.3 Modified Moment Estimation	336
	13.2 Weibull Distributions	337
	13.3 Extreme Value Distributions	339
	13.4 Normal Distribution	339
	13.5 Burr-XII Distribution	341
	13.6 Logistic Distributions	342
	Chapter14 Progressive Hybrid and Adaptive Censoring and RelatedInference	343
	14.1 Likelihood Inference for Type-I Progressive Hybrid Censored Data	344
	14.1.1 Likelihood Inference for Two-Parameter Exponential Distributions	344
	Location Parameter Known	344
	Confidence Intervals	345
	Location Parameter Unknown	348
	14.1.2 Other Distributions	350
	14.2 Likelihood Inference for Type-II Progressive Hybrid Censored Data	351
	14.2.1 Exponential Distribution	351
	14.2.2 Other Distributions	352
	14.3 Inferential Results for Adaptive Progressive Type-IICensoring	352
	14.3.1 Ng–Kundu–Chan Model	354
	14.3.2 Progressive Censoring with Random Removals	355
	Chapter15 Bayesian Inference for Progressively Type-II Censored Data	357
	15.1 Exponential and Weibull Distributions	358
	15.2 Rayleigh Distribution	363
	15.3 Pareto Distribution	365
	15.4 Burr Distributions	367
	15.5 Other Distributions	368
	Chapter16 Point Prediction from Progressively Type-II Censored Samples	370
	16.1 Prediction Concepts	370
	16.2 Prediction of Failure Times of Censored Units	372
	16.2.1 Exponential Distribution	373
	Scale Parameter >0 Known	374
	Scale Parameter >0 Unknown	375
	16.2.2 Extreme Value Distribution	378
	Scale Parameter >0 Known	379
	Scale Parameter >0 Unknown	379
	16.2.3 Normal Distribution	381
	Location Parameter ? Known	381
	Location Parameter ? Unknown	381
	16.2.4 Pareto Distributions	384
	16.3 Prediction of Future Observations	387
	16.3.1 Linear Prediction	387
	16.3.2 Bayesian Prediction	388
	Bayesian Prediction: One-Sample Case	389
	Bayesian Prediction: Two-Sample Case	390
	Chapter17 Statistical Intervals for Progressively Type-II Censored Data	393
	17.1 Exact Confidence Intervals	393
	17.1.1 Exponential Distribution	393
	17.1.2 Weibull Distribution	398
	17.1.3 Pareto Distribution	402
	17.1.4 Other Parametric Distributions	405
	17.1.5 Nonparametric Confidence Intervals for Quantiles	406
	17.1.6 An Excursus: Two-Sample Nonparametric Confidence Intervals from Type-II Censored Data	412
	17.2 Conditional Statistical Intervals	416
	17.2.1 Inference in a General Location–Scale Family	416
	Conditional Confidence Intervals for Location and Scale Parameters	417
	Conditional Confidence Intervals for Quantiles	418
	Conditional Confidence Intervals for Reliability	419
	Conditional Prediction Intervals for Future Failure Times	419
	17.2.2 Exponential Distribution	420
	17.2.3 Extreme Value Distribution	420
	17.2.4 Log-Gamma Distribution	423
	17.2.5 Pareto Distribution	424
	17.2.6 Laplace Distribution	425
	17.2.7 Other Distributions	428
	17.3 Asymptotic Confidence Intervals	428
	17.4 Prediction Intervals	429
	17.4.1 Nonparametric Prediction Intervals	429
	17.4.2 Parametric and Bayesian Prediction	429
	Prediction Intervals for Censored Failure Times	430
	Prediction Intervals for Future Observations in the Same Sample	430
	Prediction Intervals for Observations of an Independent Future Sample from the Same Population	431
	17.5 Nonparametric Tolerance Intervals	432
	17.6 Highest Posterior Density Credible Intervals	432
	Chapter18 Progressive Type-I Interval Censored Data	434
	18.1 Parametric Inference	434
	18.2 Optimal Inspection Times	437
	18.3 Optimal Progressive Interval Censoring Proportions	438
	Chapter19 Goodness-of-Fit Tests in Progressive Type-II Censoring	439
	19.1 Tests on Exponentiality	439
	19.2 Goodness-of-Fit Tests for Other Distributional Assumptions	443
	19.2.1 Methods Based on Spacings and Deviation from the Uniform Distribution	443
	19.2.2 Tests Based on Empirical Distribution Function	446
	19.2.3 Tests Based on Kullback–Leibler Distance	448
	Chapter20 Counting and Quantile Processes and Progressive Censoring	450
	20.1 Counting Process Approach	450
	20.1.1 Semiparametric Proportional Hazards Model	458
	20.2 Quantile Process Approach	459
	Chapter21 Nonparametric Inferential Issues in Progressive Type-IICensoring	462
	21.1 Precedence-Type Nonparametric Tests	462
	21.1.1 Precedence-Type Nonparametric Tests with Progressive Censoring	463
	Distribution of Test Statistics	465
	Precedence-Type Test Based on Kaplan–Meier Estimator of Cumulative Distribution Function	467
	Two Progressively Censored Samples	469
	21.1.2 Tests for Hazard Rate Ordering	472
	Part III Applications in Survival Analysis and Reliability	476
	Chapter22 Acceptance Sampling Plans	477
	22.1 Exponential Distribution	478
	22.1.1 Acceptance Sampling Plans Without Consumer Risk	478
	One-Sided Sampling Plans	479
	Two-Sided Sampling Plans	481
	22.1.2 Acceptance Sampling Plans with Consumer Risk	482
	22.1.3 Bayesian Variable Sampling Plans with Progressive Hybrid Censoring	484
	22.2 Weibull Distribution	485
	22.3 Log-Normal Distribution	486
	22.4 Reliability Sampling Plans for Interval Censored Data	486
	22.5 Capability Indices	487
	22.5.1 Exponential Progressively Type-II Censored Order Statistics	487
	22.5.2 Other Distributions	490
	Chapter23 Accelerated Life Testing	491
	23.1 Step-Stress Models	491
	23.1.1 Inference for Simple Step-Stress Model Under Progressive Type-II Censoring	493
	Progressively Type-II Censored Step-Stress Data	493
	Likelihood Function and Maximum Likelihood Estimation	495
	Exact Conditional Distributions of MLEs	496
	Confidence Intervals for 1 and 2	499
	Optimal Censoring and Optimal Test Plan	500
	23.1.2 Inference for a Simple Step-Stress Model with Random Change Under Progressive Type-II Censoring	500
	Connection to Sequential Order Statistics	502
	Parametrization via Log-Linear Link Function	503
	23.1.3 Inference for Multiple Step-Stress Model Under Progressive Type-I Censoring	505
	Progressively Type-I Censored Step-Stress Data	505
	Likelihood Function and MLEs	505
	Optimal Step-Stress Test	508
	A Modified Progressive Censoring Scheme and Optimal Step-Stress Test	509
	Step-Stress Test with Link Function Based on Box–Cox Transformation	510
	Progressively Type-I Interval Censored Exponential Data	511
	23.1.4 Multiple Step-Stress Model with Progressive Censoring: An Approach Based on Sequential Order Statistics	513
	23.2 Progressive Stress Models	513
	Chapter24 Stress–Strength Models with Progressively Censored Data	516
	24.1 Exponentially Distributed Stress and Strength	517
	24.1.1 Exponentially Distributed Stress and Strength with Known Location Parameter	517
	24.1.2 Exponentially Distributed Stress and Strength with Common Unknown LocationParameter	518
	24.2 Further Stress–Strength Distributions	521
	Chapter25 Multi-sample Models	523
	25.1 Competing Risk Models	523
	25.1.1 Model and Notation	523
	25.1.2 Exponential Distribution	524
	25.1.3 Weibull Distributions	528
	25.1.4 Lomax Distribution	530
	25.2 Joint Progressive Censoring	531
	25.3 Concomitants	533
	25.3.1 Missing Information Principle and EM-Algorithm	535
	25.4 Progressively Censored Systems Data	536
	25.4.1 Progressive First-Failure Censoring: Series Systems	537
	25.4.2 Parallel Systems	537
	Chapter26 Optimal Experimental Designs	539
	26.1 Preliminaries	540
	26.2 Probabilistic Criteria	542
	26.3 Precision of Estimates	544
	26.3.1 Exponential Distribution	546
	26.3.2 Generalized Pareto Distributions	546
	26.3.3 Extreme Value Distribution	550
	26.3.4 Further Distributions	550
	26.4 Maximum Fisher Information	552
	26.4.1 Single Parameter Case	552
	Optimal One-Step Plans	554
	State of the Art	558
	26.4.2 Two-Parameter Case	559
	26.4.3 Asymptotically Optimal Censoring Schemes	565
	26.4.4 Maximum Fisher Information Plans in Progressive Hybrid Censoring	567
	26.5 Other Optimality Criteria and Approaches	567
	26.5.1 Maximum Entropy Plans	567
	26.5.2 Optimal Estimation of Quantiles	568
	26.5.3 Optimization Based on Pitman Closeness	570
	26.5.4 Optimal Block Censoring	573
	Computational Results	576
	26.5.5 Other Criteria for Optimal Censoring Plans	578
	Appendix A Distributions	579
	A.1 Definitions of Distributions	579
	A.2 Definitions and Preliminaries	582
	A.2.1 Quantile Function	582
	A.2.2 Stochastic Orders	583
	Univariate Stochastic Orders	583
	A.2.2.1 Multivariate Stochastic Orderings	585
	Orderings of Real Vectors	586
	Appendix B Additional Demonstrative Data Sets	587
	B.1 Progressively Type-II Censored Data	587
	B.2 Progressively Type-I Censored Data	589
	Notation	593
	References	598
	Author Index	636
	Index	646