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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, and hydraulic systems in aviation industry. 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∞, and the limiting profit per unit time ω, using semi-Markov processes, when all distributions are exponential. As anticipated, to maximize A∞, the expert should repair all failed units. To maximize ω, 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 ω.
Highlights
Let us begin with two motivating applications of our general model:(1) Pumps are of paramount importance in the chemical industry as they are essential to transfer highly corrosive and abrasive chemicals through pipes
We demonstrate that the system with two spare units has higher A∞ and ω compared to a system with only one spare unit
In a situation where component lifetime is short and repair time is long, multiple spare units are necessary to improve the reliability characteristics of the system. In this extended set up, we study the limiting availability and the limiting profit per unit time when lifetime and repair times are exponentially distributed
Summary
Let us begin with two motivating applications of our general model:. (1) Pumps are of paramount importance in the chemical industry as they are essential to transfer highly corrosive and abrasive chemicals through pipes. She fixes only one failed unit during each visit; and she lets the regular repairer attend to the waiting failed unit(s), if any This second possibility we call the single repair by expert (SRE) policy. The limiting profit per unit time is defined as the long-run difference between the net revenue earned and the repair cost paid to the repair persons, including a trip charge payable to the expert, all expressed per unit time. Assuming exponential life- and repair times, they obtain A∞ and ω using the technique of semi-Markov processes (SMP) We extend their results to the case of two spare units. We obtain a threshold value for the cost per unit time payable to the expert repairer such that so long as the expert charges less than this threshold value the MRE policy yields higher profit than the SRE policy, and vice versa.
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