# A Repairable System Supported by Two Spare Units and Serviced by Two Types of Repairers

## TL;DR

This paper models a repairable system with two spares and two repairer types, analyzing optimal repair strategies and patience times to maximize availability and profit using semi-Markov processes.

## Contribution

It introduces a comprehensive model for a repairable system with mixed repairers and analyzes optimal repair policies and patience times for maximizing system availability and profit.

## Key findings

- Expert should repair all failed units to maximize availability.
- Deterministic patience time outperforms random patience time for profit maximization.
- Optimal number of repairs and patience times depend on cost parameters.

## Abstract

We study a one-unit repairable system, supported by two identical spare units on cold standby, and serviced by two types of repairers. The model applies, for instance, to ANSI (American National Standard Institute) centrifugal pumps in a chemical plant. The failed unit undergoes repair either by an in-house repairer within a random or deterministic patience time, or else by a visiting expert repairer. The expert repairs one or all failed units before leaving, and does so faster but at a higher cost rate than the regular repairer. Four models arise depending on the number of repairs done by the expert and the nature of the patience time. We compare these models based on the limiting availability $A_{\infty}$, and the limiting profit per unit time $\omega$, using semi-Markov processes, when all distributions are exponential. As anticipated, to maximize $A_{\infty}$, the expert should repair all failed units. To maximize $\omega$, a suitably chosen deterministic patience time is better than a random patience time. Furthermore, given all cost parameters, we determine the optimum number of repairs the expert should complete, and the optimum patience time given to the regular repairer in order to maximize $\omega$.