Modified block replacement models in discrete and continuous time

Abstract

In this study, we present modified multi-component block replacement policies. Units (items) are replaced only at prescribed times j = 1,2,... A failed unit is changed with a good one with probability a. Replacement time is negligible. Three replacement policies for models that are not represented as renewal processes are provided under this setup. Some reliability characteristics are discussed. In the first model, total control is considered. All units are controlled at time jT, j = 1,2,.... In the second model, a partial (group) control is studied in which a sample of size n, (0 < n < A) is taken from all units to inspect. And the last model deals with cyclic control: units are divided into r parties. Part}' k is controlled at time jT , j — 1,2,... where j = k (modulus r), k = l,2 ,...,r — 1 and if k is equal to zero then party r is controlled. A comparison between the partial (group) control and cyclic control is provided. We also introduced cyclic partial control which combines the partial and cyclic control policies. The cyclic partial control and cyclic control is compared as well. Cost type of functionals are considered and optimal replacement interval T* is studied as well.