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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.
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