A Method for Analyzing Maintenance Decisions Based on the Discrete Markov Chain

Production systems are stopped due to malfunctions such as rotting equipment, imbalance of rotating parts, and high vibration, which leads to loss of customers, reduction of market share and unemployment of personnel. In this research, using the absorbing Markov process, a mathematical model is formulated to analyze the maintenance policy of the production process, through which one of the four states of new, old, or failure due to deterioration or sudden failure can be allocated to the machine. It is assumed that the machine changes from one state to another with different probabilities, which are determined using a discrete Markov chain. The different maintenance policies can be analyzed to minimize the average production cost. The mathematical model is obtained using discrete Markov chain equations, and the optimal maintenance and repair policy can be analyzed by considering all types of costs, including maintenance, production, and failure costs, so that the average cost of the production process can be minimized.