On the Foundations of Reliability

Abstract

Under the framework of a stochastic point process of failures, this paper discusses basic ways to characterize reliability. The distinction between the failure rate of a process, useful for repairable systems, and the failure rate of a distribution, useful for nonrepairable systems, is drawn. The paper then concentrates on modeling the wearout characteristics of repairable system reliability. Neither the homogeneous Poisson nor the renewal processes will suffice for this purpose. The nonhomogeneous Poisson process is appealing as a general wearout model, but it too has nonintuitive features; for example, the distribution of first failure determines the entire process. This leads us to search for other alternatives and to consider the reliability characteristics of general point processes of failures. Results pertaining to the appealing alternative of superimposed processes are reviewed.