1 Accurate Estimation with One Order Statistic
1.1 Introduction
1.2 The Case of the Exponential Distribution
1.3 An Example for the Exponential Distribution
1.4 The Rayleigh and Weibull Distribution Extensions
1.5 Simulations and Computational Issues
1.6 Implications for Design of Life Tests
1.7 Conclusions
2 On the Inverse Gamma as a Survival Distribution
2.1 Introduction
2.2 Probabilistic Properties
2.3 Statistical Inference
2.3.1 Complete Data Sets
2.3.2 Censored Data Sets
2.4 Conclusions
3 Order Statistics in Goodness-of-Fit Testing
3.1 Introduction
3.3 Computation of the P-Vector
3.4 Goodness-of-Fit Testing
3.5 Power Estimates for Test Statistics
3.6 Further Research
4 The "Straightforward" Nature of Arrival Rate Estimation?
4.1 Introduction
4.1.1 Sampling Plan 1: Time Sampling
4.1.2 Sampling Plan 2: Count Sampling
4.1.3 Sampling Plan 3: Limit Both Time and Arrivals
4.2 Conclusions
5 Survival Distributions Based on the Incomplete Gamma Function Ratio
5.1 Introduction
5.2 Properties and Results
5.3 Examples
5.4 Conclusions
6 An Inference Methodology for Life Tests with Full Samples or Type II Right
Censoring
6.1 Introduction and Literature Review
6.2 The Methodology for Censored Data
6.3 The Uniformity Test Statistic
6.4 Implementation Using APPL
6.5 Power Simulation Results
6.6 Some Applications and Implications
6.7 Conclusions and Further Research
7 Maximum Likelihood Estimation Using Probability Density Functions of Order
Statistics
7.1 Introduction
7.2 MLEOS with Complete Samples
7.3 Applying MLEOS to Censored Samples
7.4 Conclusions and Further Research
8 Notes on Rank Statistics
8.1 Introduction
8.2 Explanation of the Tests
8.3 Distribution of the Test Statistic Under H0
8.4 WilcoxonPowerCurvesforn=2
8.5 Generalization to Larger Sample Sizes
8.6 ComparisonsandAnalysis
8.7 The Wilcoxon–Mann–Whitney Test
8.8 Explanation of the Test
8.9 Three Cases of the Distribution of W under H0
8.9.1 Case I: No Ties
8.9.2 Case II: Ties Only Within Each Sample
8.9.3 Case III: Ties Between Both Samples
8.10 Conclusions
9 Control Chart Constants for Non-Normal Sampling
9.1 Introduction
9.2 Constants d2, d3
9.3 Constants c4, c5
9.3.1 Normal Sampling
9.3.2 Non-Normal Sampling
9.4 Conclusions
10 Linear Approximations of Probability Density Functions
10.1 Approximating a PDF
10.2 Methods for Endpoint Placement
10.2.1 Equal Spacing
10.2.2 Placement by Percentiles
10.2.3 Curvature-Based Approach
10.2.4 Optimization-Based Approach
10.3 Comparison of the Methods
10.4 Application
10.4.1 ConvolutionTheorem
10.4.2 Monte Carlo Approximation
10.4.3 Convolution of Approximate PDFs
10.5 Conclusions
11 Univariate Probability Distributions
11.1 Introduction
11.2 Discussion of Properties
11.3 Discussion of Relationships
11.3.1 Special Cases
11.4 The Binomial Distribution
11.5 The Exponential Distribution
11.6 Conclusions
12 Moment-Ratio Diagrams for Univariate Distributions
12.1 Introduction
12.2 Reading the Moment-Ratio Diagrams
12.3 The Skewness-Kurtosis Diagram
12.4 The CV-Skewness Diagram
12.5 Application
12.6 Conclusions and Further Research
13 The Distribution of the Kolmogorov–Smirnov, Cramer–von Mises, and Anderson–
Darling Test Statistics for Exponential Populations with Estimated Parameters
13.1 The Kolmogorov–Smirnov Test Statistic
13.1.1 Distribution of D1 for Exponential Sampling
13.1.2 Distribution of D2 for Exponential Sampling
13.2 Other Measures of Fit
13.2.1 Distribution of W12 and A21 for Exponential Sampling
13.2.2 Distribution of W2 and A2 for Exponential Sampling
13.3 Applications
14 Parametric Model Discrimination for Heavily Censored Survival Data
14.1 Introduction
14.2 Literature Review
14.3 A Parametric Example
14.4 Methodology
14.4.1 Uniform Kernel Function
14.4.2 TriangularKernelFunction
14.5 Monte Carlo Simulation Analysis
14.6 Conclusions and Further Work
15 Lower Confidence Bounds for System Reliability from Binary Failure Data Using
Bootstrapping
15.1 Introduction
15.2 Single-Component Systems
15.3 Multiple-Component Systems
15.4 Perfect Component Test Results
15.5 Simulation
15.6 Conclusions
