Published date: Jul 24 2024

Journal Title: ESPOCH Congresses: The Ecuadorian Journal of S.T.E.A.M.

Issue title: Volume 3, Issue 3

Pages: 122–150

DOI: 10.18502/espoch.v3i3.16618

A Sánchez-Herguedas - antoniosh@us.es

F Rodrigo-Muñoz

This study aims to develop a tool that calculates the optimal preventive maintenance interval when the income from the operation of an asset changes. The income can be modified by market disturbances or by the decrease in the efficiency of the asset due to its degradation. A system with four states is designed to model the operation and maintenance process: operational, corrective, preventive, and degraded operation is mathematically modeled. The system evolves over time, according to a semi-Markovian process. The transitions and sojourn times between each state produce the accumulation of costs and income as returns (negative or positive) in a variable called average accumulated return. The average accumulated return is defined by a system of difference equations that are solved by applying the ztransform. The solution is a function that is dependent on the preventive interval. By derivation, the mathematical expression of the optimal preventive interval that maximizes the average accumulated return is obtained. From this expression, it can be deduced that the size of the optimal preventive interval is directly affected by the income from the asset operation. Higher income increases the size and lower income decreases it. For this reason, the maintenance manager must observe the changesoccuring in the income from the use of his equipment in order to optimize his management economically.

Keywords: preventive interval, income, semi-Markovian model, Wiener process.

Resumen

Se presenta una herramienta que calcula el intervalo de mantenimiento preventivo óptimo, cuando se modifica el ingreso obtenido por el funcionamiento de un activo. El ingreso se puede modificar por alteraciones del mercado, o por la disminución de la eficiencia del activo debido a su degradación. Para reflejar el proceso de operación y mantenimiento se modela matemáticamente un sistema con cuatro estados: operativo, correctivo, preventivo y operativo degradado. El sistema evoluciona en el tiempo, según un proceso semi-markoviano. Las transiciones y los tiempos de permanencia entre cada estado provocan la acumulación de costes e ingresos como retornos (negativos o positivos) en una variable llamada retorno medio acumulado. El retorno medio acumulado se define por un sistema de ecuaciones en diferencias que se resuelve aplicando la transformada z. La solución es una función que depende del intervalo preventivo y de la que por derivación se obtiene la expresión matemática del intervalo preventivo óptimo que maximiza el retorno medio acumulado. De esta expresión se deduce que el ingreso por el uso de un activo afecta directamente al tamaño del intervalo preventivo óptimo. Un mayor ingreso aumenta el tamaño y un menor ingreso lo disminuye. Por este motivo, el responsable de mantenimiento debe observar las modificaciones que se producen en los ingresos por el uso de sus equipos, con objeto de optimizar económicamente su gestión.

Palabras Clave: Intervalo preventivo, Ingresos, Modelo Semi-markoviano, Estado-degradado.

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