This chapter reviews fundamental ideas in reliability theory and inference. The first part of the chapter accounts for lifetime distributions that are used in engineering reliability analyis, including general properties of reliability distributions that pertain to lifetime for manufactured products. Certain distributions are formulated on the basis of simple physical properties, and other are more or less empirical. The first part of the chapter ends with a description of graphical and analytical methods to find appropriate lifetime distributions for a set of failure data.

The second part of the chapter describes statistical methods for analyzing reliability data, including maximum likelihood estimation and likelihood ratio testing. Degradation data are more prevalent in experiments in which failure is rare and test time is limited. Special regression techniques for degradation data can be used to draw inference on the underlying lifetime distribution, even if failures are rarely observed.

The last part of the chapter discusses reliability for systems. Along with the components that comprise the system, reliability analysis must take account of the system configuration and (stochastic) component dependencies. System reliability is illustrated with an analysis of logistics systems (e.g., moving goods in a system of product sources and retail outlets). Robust reliability design can be used to construct a supply chain that runs with maximum efficiency or minimum cost.

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Copyright © 2006 Springer-Verlag. This book chapter first appeared in Springer Handbook of Engineering Statistics, Edited by Hoang Pham, 49-61, London: Springer-Verlag, 2006

The definitive version is available at: Springer-Verlag

Full Citation:

Kvam, Paul H., and Jye-Chyi Lu. "Statistical Reliability with Applications." In Springer Handbook of Engineering Statistics, edited by Hoang Pham, 49-61. London: Springer-Verlag, 2006.