Finite time preventive maintenance optimization by using a Semi-Markov process with a degraded state. A case study for diesel engines in mining

During the design of maintenance plans for an asset, the frequency calculation of preventive interventions is a maintenance engineer's essential task. This document presents a tool (mathematical formula) to calculate the preventive maintenance interval. The tool considers the maintenance costs and the income generated for the company by its use. Managers can benefit from its simple application to gain efficiency. Typically, business projects are executed over a period. The tool calculates the optimal interval for any given project duration. It also allows the analysis of the size of the preventive interval when the income received changes. This change may be due to asset impairment or changes in the market price of the business product. For the development of the tool, a semi-Markovian model is designed with four states representing the operation and maintenance of the asset. The asset evolves by transiting between states and accumulating costs and income in the form of returns. From the model, a system of difference equations is developed whose variable is the expected accumulated return at any transition, and the z-transform is used to solve it. Deriving its mathematical expression, the formula for the preventive interval that maximizes the expected accumulated return is obtained. Both formulae are used in a case study. Taking advantage of the degraded state, it is shown that higher income increases the interval size while lower-income decreases it. The limits of these variations are also established. Simulation and numerical methods are used to validate analytic results.