Optimum problems in backward times of reliability models

Abstract

This paper considers the problem of searching for the actual time of failure for a system when the only information that is available is that it is has failed by a time t. This situation can be analyzed by using the concept of the reversed failure rate. This paper considers optimization problems that can be solved by using the reversed failure rate. When a unit is detected to have failed at time t, we discuss an optimum backward time from time t to search for its failure time which minimizes the expected cost. The recovery of a database system and of reweighing products using a scale are taken to be two typical applications of the backward time concept. Two models are proposed for appropriate maintenance actions for these situations when a unit is detected to have failed at time t.