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Optimizing repair/replacement policy if cumulative distribution function of time-to-repair is rational function

Malinowski Jacek

Safety and Reliability of Systems and Processes

2023

Summer Safety and Reliability Seminar 2023

147--156

A problem of finding the optimal repair/replacement policy of a technical object is under investigation. Depending on the distribution of the time-to-repair and certain cost parameters, a decision is taken whether to repair a failed object or replace it immediately after it fails. If a repair is chosen and it is not completed within a certain period, it is interrupted and the object is replaced by a new one. The optimization task consists in formulating the conditions for choosing between immediate replacement and repair, and deriving the analytical equation for the maximum duration of a repair. The objective function is the expected cost of restoring the object to the operating condition. It is assumed that the cumulative distribution function (CDF) of the time-to-repair is a rational function (a quotient of polynomials). The properties of such CDFs are analyzed and the solutions of several optimization tasks with different CDFs that are rational functions are presented. The issue of fitting the time-to-repair distribution to empirical data is also addressed.