Markov Chain Cost/Life-Cycle Model

Abstract

In maintenance management, predictive and preventive strategies are considered essential for the purpose of improving the overall efficiency of the systems, and for extending the operational lifespan of equipment. Stochastic behavior of a system's maintenance states can be effectively modeled with Markov chains, a mathematical framework providing the needed capability. With this approach for calculation of the system state probabilities for specific time intervals, maintenance planners can determine future conditions and plan maintenance schedules better. The following paper looks into the Markov chain deployment in maintenance optimization. The first step is to determine a set of discrete states that would represent the condition of a piece of equipment at any given time. Such conditions cover a wide spectrum, from sustainable to completely dysfunctional ones. Then, probabilities of the transition between these states are determined using historical maintenance data and equipment condition. Through implementing these probabilities, we model behavior of the system with time and find the most profitable maintenance policies. Our approach involves the construction of a state-transition matrix and its solution for steady – state probabilities to assess the long-term behavior of the equipment under various condition based maintenance strategies. Another cost function that includes the costs of distinct maintenance actions and the implications of equipment failure is presented as well. Through this optimization process, we determine the ideal maintenance plan which leads to the minimization of total operational expenditures as well as maximum equipment reliability. The results show that the use of the Markov chain optimization maintenance is a remarkable tool for improving decision-making processes in maintenance management thus resulting to an analytical technique used for increasing equipment uptime and reducing maintenance-related costs. This method turns out to be very effective in industries where the cost of equipment failure is very high and efficiency of production is the main trend. The paper is concluded with case studies and suggestions for building the Markov chain models into the current maintenance management systems.