  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 $\omega$.
