Reliability is an essential concept in mathematics, computing, research, and all disciplines of engineering, and reliability as a characteristic is, in fact, a probability. Therefore, in this book, the author uses the statistical approach to reliability modelling along with the MINITAB software package to provide a comprehensive treatment of modelling, from the basics through advanced modelling techniques.
The book begins by presenting a thorough grounding in the elements of modelling the lifetime of a single, non-repairable unit. Assuming no prior knowledge of the subject, the author includes a guide to all the fundamentals of probability theory, defines the various measures associated with reliability, then describes and discusses the more common lifetime models: the exponential, Weibull, normal, lognormal and gamma distributions. She concludes the groundwork by looking at ways of choosing and fitting the most appropriate model to a given data set, paying particular attention to two critical points: the effect of censored data and estimating lifetimes in the tail of the distribution.
The focus then shifts to topics somewhat more difficult:
The final chapter provides snapshot introductions to a range of advanced models and presents two case studies that illustrate various ideas from throughout the book.
Introduction
Events and Probability
Rules of Probability
Dependent Events
Random Variables and Probability Distributions
The Reliability Function
The Hazard Function
Expectation
COMMON LIFETIME MODELS
Introduction
The Poisson Process
The Weibull Distribution
The Gumbel Distribution
The Normal and Lognormal Distributions
The Gamma Distribution
The Logistic and Log Logistic Distributions
The Pareto Distribution
Order Statistic and Extreme Value Distributions
MODEL SELECTION
Introduction
Non-Parametric Estimation of R(t) and h(t)
Censoring
Kaplan-Meier Estimator
Graphical Methods
Straight Line Fitting
Weibull Plotting
Normal Plotting
Other Model Family Plots
Comparison of Distributions
MODEL FITTING
Parameter Estimation
The Variance of Estimators
Confidence Interval Estimates
Maximum Likelihood
Estimating Quantities
Estimation Methods Using Sample Moments
General Probability Plots
Goodness of Fit
Pearson's Chi-squared Test
Kolmogorov-Smirnov Test
Tests for Normality
A-squared and W-squared Tests
Stabilized Probability Plots
Censored Data
REPAIRABLE SYSTEMS
Introduction
Graphical Methods
Testing for Trend
Repair Time
Maintainability and Availability
Introduction to Renewal Theory
Laplace Transforms
The Renewal Function
Alternating Renewal Processes
The Distribution of N(t)
SYSTEM RELIABILITY
Systems and System Logic
Tie and Cut Sets
Probability Bounds
Fault Trees
Failure Over Time
Redundancy
Quorum or m-out-of-n Systems
Analysis of Systems Using State Spaces
Mean Time to Fail (MTTF)
Considerations Due to "Switching"
Common Cause Failures
MODELS FOR FUNCTIONS OF RANDOM VARIABLES
Combinations and Transformations of Random Variables
Expectations of Functions of Random Variables
Approximations for E[g(x)] and V[g(x)]
Distribution of a Function of Random Variables
Probabilistic Engineering Design
Stress and Strength Distributions
Interference Theory and Reliability Computations
Normally Distributed Stress and Strength
Safety Factors and Reliability
Graphical Approach for Empirically Determined Distributions
MAINTENANCE STRATEGIES
Maintained Systems
Availability
Markovian Systems
Mean Time between Failures (MTBF)
Age Replacement
Scheduled Maintenance
Systems with Failure Detection/Fail Safe Devices
Down-Time Distributions
LIFE TESTING AND INFERENCE
Life Test Plans
Prediction of Time on Test
Inference for the Exponential Distribution
The Effect of Data Rounding
Parametric Reliability Bounds
Likelihood-Based Methods
The Likelihood Ratio Test
Binomial Experiments
Non-Parametric Estimation and Confidence Intervals for R(t)
Estimating System Reliability from Subsystem Test Data
Accelerated Testing
ADVANCED MODELS
Covariates
Proportional Hazards Models
Accelerated Life Models
Mixture Models
Competing Risks
Dependent Failures
Load-Sharing Systems
Bayesian Reliability
Case Studies
USEFUL MATHEMATICAL TECHNIQUES
Partial Fractions
Series
Taylor Expansions
Newton-Raphson Iteration
Numerical Integration
Matrix Algebra
The Principle of Least Squares
Biography
Wolstenholme, Linda C.
"This is a lucid introduction to many important ideas in reliability. In describing the various models and techniques the author includes plenty of practical advice about their usuage. Frequent and well-developed examples illustrate and extend the techniques and there are two brief case studies at the end of the book. By studying these examples carefully, the student will learn much about the difficult art of formulating useful models."
--Biometrics, June 2000