Probability Distributions Used in Reliability Engineering

This book, developed by the University of Maryland Center for Risk and Reliability, published by the RIAC, and used as a supplemental reference book in courses offered by the University of Maryland, provides details on 22 probability distributions. Each distribution section provides a graphical visualization and formulas for distribution parameters, along with distribution formulas. Common statistics such as moments and percentile formulas are followed by likelihood functions and in many cases the derivation of maximum likelihood estimates. Bayesian non-informative and conjugate priors are provided followed by a discussion on the distribution characteristics and applications in reliability engineering. Each section is concluded with online and hardcopy references which can provide further information followed by the relationship to other distributions.

The book is divided into six parts. Part 1 provides a brief coverage of the fundamentals of probability distributions within a reliability engineering context. Part 1 is limited to concise explanations aimed to familiarize readers. For further understanding the reader is referred to the references. Part 2 to Part 6 cover Common Life Distributions, Bathtub Distributions, Univariate Continuous Distributions, Univariate Discrete Distributions and Multivariate Distributions respectively.

This book refers to software available at www.enre.umd.edu/tools.htm aimed at students and academic staff which allow users to:

• Plot distributions and interactively vary distribution parameters to provide understanding on the effect each parameter has on the probability distribution function, cumulative distribution function and hazard rate.
• Export probability distribution plots directly to the printer, picture or to a chart object in Microsoft Excel.

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