A Generalized Sequential Preventive Maintenance Policy for a System

Abstract

This paper proposes and analyzes a generalized sequential preventive maintenance policy for a system subject to shocks. The shocks arrive according to a non-homogeneous Poisson process {[file:////NT-SERVER-402/www122/ Image31.gif];[file:////NT-SERVER-402/www122/Image32.gif]}, whose intensity function [file:////NT-SERVER-402/www122/Image33.gif] varies with the number of preventive maintenance actions [file:////NT-SERVER-402/www122/Image34.gif]that have already been carried out, and the time [file:////NT-SERVER-402/www122/ Image35.gif]that has elapsed since the last preventive maintenance action. Upon the arrival of a shock, the system is maintained preventively or repaired minimally with probability [file:////NT-SERVER-402/www122/Image36.gif] and [file:////NT-SERVER-402/www122/Image37.gif] respectively depending on the number of preventive maintenance actions [file:////NT-SERVER-402/www122/ Image38.gif]and shocks [file:////NT-SERVER-402/www122/Image39.gif]that have already occurred. In addition, a planned preventive maintenance is carried out as soon as [file:////NT-SERVER-402/www122/Image40.gif]time units have elapsed since the [file:////NT-SERVER-402/www122/Image41.gif]1[file:////NT-SERVER-402/ www122/Image42.gif]th preventive maintenance action. If [file:////NT-SERVER- 402/www122/Image43.gif]N, the system is replaced rather than maintained preventively. The objective is to determine the optimal plan (in terms of [file:////NT-SERVER-402/www122/Image17.gif]and [file:////NT-SERVER-402/www122/ Image44.gif]) which minimizes expected cost per unit of time. It is shown that under certain reasonable assumptions, sequential preventive maintenance policy has unique solutions. Various special cases are considered.