Limiting Performance of a One-unit System under Various Repair Models

Jyotirmoy Sarkar
Abstract
We study the limiting availability of a one-unit system supported by an identical spare unit. A failed unit is perfectly repaired by an in-house person, if doable within a random or deterministic patience time, or else by a visiting expert. When all distributions are exponential, using semi-Markov processes (SMP), we show that a deterministic patience time is preferable to a random patience time, and characterize conditions under which the expert should repair multiple failed units (rather than only one failed unit) during each visit. We generalize the results to the case of arbitrary continuous life and repair time distributions. Our technique involves extending the limiting probability theorem of a semi-Markov process to that of an extended semi-Markov process.