Reliability Modelling : A Statistical Approach book cover
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Reliability Modelling
A Statistical Approach





ISBN 9781584880141
Published June 25, 1999 by Chapman and Hall/CRC
272 Pages

 
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Book 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.
  • 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

    ...
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    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