## A Markov Method for the Optimum Preventive Maintenance of a Component

A. Jayakumar and S. Asgarpoor (USA)

### Keywords

Preventive maintenance, optimizationtechnique, Markov modeling, major maintenance, minormaintenance, deterioration, random failure, optimalpolicy.

### Abstract

In traditional maintenance approaches, pre defined activities were carried out at regular intervals. This approach was not cost-effective and did not extend component lifetime as much as possible [1]. In the last few years, utilities have employed flexible programs based on an analysis of needs and priorities, or on a study of information obtained through predictive maintenance. However, this approach that is referred to as Reliability Centered Maintenance (RCM), is considered heuristic, and its application requires experience and involves time consuming data collection [5]. Preventive Maintenance is a significant function within the overall operational environment in electric power systems. A reliable and cost-effective maintenance program ensures that preventive maintenance is performed at optimal levels. The problem of replacement or overhaul of equipment, which deteriorates with usage, is one of the standard applications of Markov processes. In this paper, a component with deterioration and random failure is modeled using Markov processes. The model incorporates the concept of minor and major preventive maintenance with the objective of determining optimal mean times to preventive maintenance (both minor and major) by maximizing the availability of the component. Mathematical optimization programs such as Maple 7 and Lingo 7 are used to find the optimal solution, which is illustrated using a numerical example. Also an optimal maintenance policy is obtained using Markov decision processes. Recently, however, several mathematical models are being utilized in maintenance scheduling. In the literature on maintenance optimization models it is stated that ". . . there are a number of case studies published which show that mathematical models are a good means to achieve both effective and efficient maintenance" [7]. In power systems, Markov chains have been extensively applied to the mathematical modeling of reliability and maintenance problems.