Comparisons of replacement policies

Maintenance comparisons: block policies

Complete repair and minimal repair models with a block maintenance policy are considered. Each of these models gives rise to a counting process, and these processes are compared stochastically. This contrasts with most previous work on maintenance policies where only univariate marginal comparisons were made. Also a more general block schedule is considered than is customary.

On stochastic ordering of random vectors

Conditions that have been widely used to establish stochastic ordering of random vectors include those given by Kamae et al. (1977), Barlow and Proschan (1975) and Langberg (1988). In this note we offer conditions that are weaker than those above, thus providing potential application to a wider class of problems.

Stochastic comparison of repairable systems by coupling

Stochastic comparison results for replacement policies are shown in this paper using the formalism of point processes theory. At each failure moment a repair is allowed. It is performed with a random degree of repair including (as special cases) perfect, minimal and imperfect repair models. Results for such repairable systems with schemes of planned replacements are also shown. The results are obtained by coupling methods for point processes.

Comparison of replacement policies via point processes

First, some basic concepts from the theory of point processes are recalled and expanded. Then some notions of stochastic comparisons, which compare whole processes, are introduced. The use of these notions is illustrated by stochastically comparing renewal and related processes. Finally, applications of the different notions of stochastic ordering of point processes to many replacement policies are given.