Maintenance comparisons: block policies

Abstract

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.

Comparison of maintenance policies with monotone failure rate distributions

“…In these papers it was assumed that the distribution F is new better than used (NBU) or new worse than used (NWU). We assume that the distribution of the life time of the system F is either increasing failure rate (IFR) or decreasing failure rate (DFR) and show how the comparisons differ from those obtained by Block et al [2,3].…”

“…To establish one of the stochastic ordering defined above, we construct a probability space with the processes * N N; * N N 0 ; such that the probability law of * N N and * N N 0 is as of N and N 0 ; respectively, and inequalities (1), (2) or (3) hold with probability 1.…”

“…The most commonly known maintenance policies are the block replacement, age replacement and minimal repair. These policies were first introduced in the literature by Barlow and Proschan [1] and Block et al [2,3].…”

“…Comparisons concerning block policies are given in References [1,2]. In Reference [3] there are comparisons between different age policies.…”

On lifetimes in random environments

“…Taking into account Definition 2.1 of Ebrahimi [6] and statement (c) in Theorem 3.1.1 of Block, Langberg, and Savits [3], assertion (i) then holds if and only if T 1 ¢ st T 2 . Hence, the proof follows from Theorem 2 above.…”