Reliability Modelling: A Statistical ApproachReliability 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. |
Contents
Basic Concepts | 1 |
Common Lifetime Models | 21 |
Model Selection | 37 |
Lognormal plot for Example 3 7 | 51 |
4 | 53 |
Log likelihood function for Example 4 2 | 60 |
PP plot for Example 4 11 | 68 |
Cumulative distribution function plot for the KolmogorovSmirnov | 76 |
An alternating renewal process | 98 |
6 | 101 |
Block diagram for Example 6 2 | 106 |
Models for Functions of Random Variations | 127 |
Maintenance Strategies | 149 |
Life Testing and Inference | 175 |
Advanced Models | 211 |
Appendix | 239 |
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Common terms and phrases
analysis approximately assumed binomial bulbs C₂ censored component confidence interval considered cost covariates data of Example data set distribution function equations exponential distribution exponential lifetime fail failure mode failure rate fibres Figure gamma distribution given Gumbel distribution hazard function hazard rate independent interval estimates lifetime model likelihood function likelihood ratio log likelihood lognormal Markov diagram maximum likelihood estimates MCCF mean mean lifetime method MINITAB modes of failure MTBF MTTF normal distribution number of failures number of observations Pi(s plot for Example Poisson process probability density function quantile random variable rate parameter redundant system reliability function repair result right-censored ROCOF S₁ S₂ sample scale parameter Section series system shown standard deviation standby statistic subsystems Suppose system failure t₁ T₂ Table tion two-unit uncensored observations unit variance weakest-link Weibull distribution Weibull model Weibull plot X₁ yields zero λδι λι λμ
Popular passages
Page 252 - Winterbottom, A. (1980) Asymptotic expansions to improve large sample confidence intervals for system reliability. Biometrika, 67, 351-7.