Statistical Analysis of Reliability and Life-testing Models: Theory and Methods, 2nd edition (Statistics: a Series of Textbooks and Monographs)

1  Probabilistic Models
     1. PROBABILITY
          1.1. Introduction
          1.2. Notation
          1.3. Definition of Probability
          1.4. Conditional Probability and Independence
          1.5. Useful Notation in Counting

     2. PROBABILITY DISTRIBUTION FUNCTIONS
          2.1. Cumulative Probability Distribution Functions
          2.2. Discrete Probability Density Funtions.
          2.3. Continuous Probability Density Functions
          2.4. Other Probability Distributions
          2.5. Joint Probability Distributions
     3. FAMILIAR UNIVARIATE PROBABILITY DISTRIBUTION FUNCTIONS
     4. PROPERTIES OF RANDOM VARIABLES
          4.1. Functions of a Random Variable
          4.2. Expectation
          4.3. Location and Scale Parameters
          4.4. Reliability Concepts
               Exercises
          4.5. Other Properties of Random Variables

2  Basic Statistical Inference
     1. INTRODUCTION
     2. ORDER STATISTICS
     3. DESCRIPTIVE STATISTICS
     4. SUFFICIENCY AND COMPLETENESS
     5. SUFFICIENCY IN THE PRESENCE OF NUISANCE PARAMETERS
     6. INVARIANCE
     7. PRINCIPLES AND METHODS OF ESTIMATION
          7.1. Loss Functions
          7.2. Other Properties of Estimators
          7.3. Principle 1. Minimax Estimator
          7.4. Principle 2. Bayes Estimator
          7.5. Principle 3. Uniformly Minimum Variance Unbiased Estimator (UMVUE)
          7.6. Principle 4. Minimum Mean Squared Error Invariant Estimators
          7.7. Principle 5. Least Squares Estimation
          7.8. Principle 6. Maximum Likelihood Estimation
     8. PRINCIPLES OF HYPOTHESIS TESTING AND INTERVAL ESTIMATION
          8.1. Test of a Statistical Hypothesis
          8.2. Confidence Interval Estimation

3  The Exponential Distribution
     1. PROPERTIES OF THE EXPONENTIAL DISTRIBUTION
          1.1. Location and Scale Parameters
          1.2. Moments and Distributional Properties
          1.3. Constant Hazard Fllllction (No-Memory Property)
          1.4. Poisson Process
          1.5. Spare Parts
          1.6. Series Systems
          1.7. Parallel Systems
          1.8. Mixed Populations
     2. STATISTICAL INFERENCES FOR ONE-PARAMETER EXPONENTIAL DISTRIBUTION; X ~ EXP(\\theta)
          2.1. Point Estimation (Complete Samples)
          2.2. Tests of Hypotheses
          2.3. Confidence Interval Estimation
          2.4. Tolerance Limits
     3. ONE-PARAMETER EXPONENTIAL DISTRIBUTION. TYPE II CENSORED SAMPLING
          3.1. Choice of Censoring Fraction
     4. ONE-PARAMETER EXPONENTIAL DISTRIBlITION. TYPE I CENSORED SAMPLING
          4 .1. Inferences Based on r
          4.2. Inferences Based on \\theta_1
          4.3. Truncated Exponential Distribution
     5. CENSORED SAMPLING WITH REPLACEMENT
          5.1. Type I Censoring with Replacement
          5.2. Type II Censoring with Replacement
     6. TWO-PARAMETER EXPONENTIAL DISTRIBUTION. TYPE II CENSORED SAMPLING (WITHOUT REPLACEMENT)
          6.1. Inferences on \\theta; \\eta Unknown
          6.2. Inferences on \\eta; \\theta Unknown
          6.3. Tolerance Limits and Confidence Limits on Reliability
     7. TWO-PARAMETER EXPONENTIAL DISTRIBUTION. TYPE II CENSORED SAMPLING (WITH REPLACEMENT)
     8. TWO-PARAMETEJ{ EXPONENTIAL DISTRIBlITION. TYPE I CENSORED SAMPLING (WITH REPLACEMENT)
          8.1. Inferences on \\theta; \\eta Unknown
          8.2. Inferences on \\eta; \\theta Unknown
     9. TWO-PARAMETER EXPONENTIAL DISTRIBlITION. TYPE I CENSORED SAMPLING (WITH0UT REPLACEMENT)
          9 .1. Inferences on \\theta; with \\eta Unknown
          9.2. Inferences on \\eta; \\theta Unknown
     10. MULTIPLE TYPE II CENSORING OR MISSING OBSERVATIONS
          10.1. Point Estimation
          10.2. Inference Procedures for EXP(\\theta) Based on a Single-Order Statistic
          10.3. Inference Procedures for EXP(\\theta; \\eta)
     11. k-SAM.PLE PROCEDURES
          11.1 Two-Sample Results
          11.2. k-Sample Results
          11.3. Differences of Failure Intensities

4  The Weibull Distribution
     1. MAXIMUM LIKELIHOOD PROCEDURES: X - WEI(\\theta, \\beta)
          1.1 Calculation of MLEs
          1.2. Pivotal Quantity Properties of the MLEs
          1.3. Monte Carlo Simulation
          1.4. Aymptotic Properties
          1.5. Inferences on \\beta; \\theta Unknown
          1.6. Inferences on \\theta; \\beta Unknown
          1.7. Tolerance Limits and Inferences on Percentiles
          1.8. Approximate Methods
     2. INFERENCES BASED ON SIMPLE ESTIMATORS
          2.1. Computation of the GLUEs
          2.2. Variances of the GLUEs
          2.3. Modified GLUEs to Minimize MSE and Approximate MLEs
          2.4. Inferential Results for \\delta or \\beta
          2.5. Inferences on R; x_1-p ; and \\theta
     3. MULTIPLE SAMPLE PROBLEMS
          3.1. Combined Sample Estimate of \\beta
          3.2. Testing Equality of Shape Parameters
          3.3. Results for Scale Parameters
          3.4. Selecting the Better of Two Weibull Populations
          3.5. Prediction Intervals
     4. THREE-PARMETER WEIBULL DISTRIBUTION
          4.1. Estimation
          4.2. Tests of Two-Parameter Exponentiality Against Three-Parameter Weibull Alternatives
          4.3. Test for Two-Parameter Weibull Versus Three-Parameter Weibull

5  The Gamma Distribution
     1. PROPERTIES OF THE GAMMA DISTRIBUTION
     2. POINT ESTIMATION
          2.1. Complete Samples; Maximum Likelihood Estimation
          2.2. Censored Sampling
          2.3. Three-Parameter Gamma Distribution
     3. ASYMPTOTIC RESULTS
     4. INFERENCES ON K
          4.1. Two-parameter Gamma Distribution
          4.2. Test of Two-Parameter Exponentiality Against a Tilree-Parameter Ganuna Alternative
     5. INFERENCES ON \\theta Win! K UNKNOWN
     6. INFERENCES ON THE MEAN

6  Extreme-Value Distributions
     1. DISTRIBUTIONAL RESULTS
     2. APPLICATIONS

7  The Logistic and Other Distributions
     1. LOGISTIC DISTRIBUTION
          1.1 Maximum Likelihood Estimation and Asymptotic Properties
          1. 2. Inferences on µ and \\sigma
          1.3. Tolerance Limits
          1.4. Inferences on Reliability
          1.5. Simple Estimators
     2. CAUCHY DISTRIBUTION
     3. NORMAL DISTRIBUTION
          3.1. Complete Samples
          3.2. Censored Sampling
     4. POLYNOMIAL HF r.IJDELS
     5. GENERALIZED GAMMA DISTRIBUTION

8  Goodness-of-Fit Tests
     1. PROBABILITY PLOTS AND LEAST SQUARES FITTING
     2. CHI-SQUARE GOODNESS OF FIT
     3. CRAMER-VON MISES TESTS
     4. LIKELIHOOD-RATIO-TYPE TESTS
          4.1. Normal Versus Two-Parameter Exponential
          4.2. Normal Versus Double Exponential
          4.3. Normal Versus Cauchy
          4.4. Weibull Versus Lognormal or Extreme Value Versus Normal

9  Repairable Systems
     1. THE WEIBULL PROCESS
          1.1. Analysis of Failure Truncated Data
          1.2. Analysis of Time Truncated Data
     2. TESTING FOR TREND IN A POISSON PROCESS
     3. COMPOUND WEIBULL PROCESSES
     4. RENEWAL PROCESSES

Appendixes
References