Abstract
Assuming exponential lifetime and repair time distributions, we study the limiting availability A∞ as well as the per unit time-limiting profit ω of a one-unit system having two identical, cold standby spare units using semi-Markov processes. The failed unit is repaired either by an in-house repairer within an exponential patience time T or by an external expert who works faster but charges more. When there are two repair facilities, we allow the regular repairer to begin repair or to continue repair beyond T if the expert is busy. Two models arise accordingly as the expert repairs one or all failed units during each visit. We show that (1) adding a second spare to a one-unit system already backed by a spare raises A∞ as well as ω; (2) thereafter, adding a second repair facility improves both criteria further. Finally, we determine whether the expert must repair one or all failed units to maximize these criteria and fulfill the maintenance management objectives better than previously studied models.
Highlights
To motivate this research, let us mention an application
The system described above operates as follows: At time t = 0, a unit is placed to function while the spare units wait on cold standby. When the functioning unit fails, a spare unit starts to operate instantly, while the dead unit is sent to the in-house repairer
When there is only one repair facility, we show that a system having two spare units attains greater A∞ as well as greater ω compared to a system having one spare
Summary
To motivate this research, let us mention an application. In the chemical industry, where pumps are essential components to transfer highly corrosive chemicals, some insurmountable costly risks are abrupt halt in the manufacturing process, catastrophic failure, and hazardous environmental interference. (our system is different than a one-out-of-three system.) When the functioning unit fails, a spare unit starts to operate instantly, while the dead unit is sent to the in-house repairer If he is not able to finish the repair within the given random patience time (RPT) T, or when the system goes down because all three units have failed, the visiting expert repairer is called in. Bieth et al [2] investigate Models (1) and (2), and those under a deterministic patience time policy (DPT)—(3) MRE-DPT and (4) SRE-DPT—when there is only one spare unit and one repair facility They assume that the life and repair times are exponentially distributed and find A∞ and ω by invoking the method called semi-Markov processes (SMP).
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