ABSTRACT
Application of measures of uncertainty to reliability theory is a recent topic of study and research. To pursue the developments in this connection, we require a brief review of the important concepts and results in reliability analysis and the associated fields. After examining the link between information theory and reliability the Chapter begins with the definitions and examples of the notions of hazard rate, mean residual life, inactivity time or reversed residual life, their examples and important properties. This is followed in Section 3 by introducing the quantile versions of these concepts. Various quantile functions that can be used as lifetime models are presented in Section 4. The reliability of a device being assessed by its ageing behavior the ageing classes generally employed in life length studies form the topic in the next three sections. Similarly, concepts based on reversed time relevant in various contexts are reviewed in Section 9. Study of reliability of systems need the results on order statistics which are discussed in Section 10. In Section 11, concave and convex distributions and in Section 12 weighted models are reviewed. Comparison of reliabilities of devices used for the same purpose has attracted much interest. Stochastic orderings of life distributions have an important role in this connection. The Chapter concludes in Section 13 by a review of significant contributions in the ordering of lifetimes.
