Reliability Modelling: A Statistical Approach, 1st Edition (Paperback) book cover

Reliability Modelling

A Statistical Approach, 1st Edition

By Linda C. Wolstenholme

Chapman and Hall/CRC

272 pages

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Paperback: 9781584880141
pub: 1999-06-25
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Description

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 difference in the analysis of lifetimes for repairable versus non-repairable systems and whether repair truly "renews" the system

  • methods for dealing with system with reliability characteristic specified for more than one component or subsystem

  • the effect of different types of maintenance strategies

  • the analysis of life test data

    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.

  • Reviews

    "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

    Table of Contents

    BASIC CONCEPTS

    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

    Subject Categories

    BISAC Subject Codes/Headings:
    BUS053000
    BUSINESS & ECONOMICS / Quality Control
    MAT029000
    MATHEMATICS / Probability & Statistics / General