Using repair-depot system reliability to determine the distribution of supportability turn-around time

assuming constant repair times, Linton, et al. (1995) used an 'expression f or the reliability of the system for repairing failed units (FU) at a repai r-depot' to compute the longest repair time for a newly failed unit (NFU) w hich assures a given reliability level (also termed the NFU supportability turn-around time, STAT) in terms of the: constant failure rate for all components, number of spares (s) on-hand, number (n) of FU either 'under repair' or 'scheduled to begin repair in the future', downstream repair completion times (DRCT) for FU. Since subtraction of the repair time for a NFU from its STAT-value yields t he NFU's latest repair start-time (LRST) which assures a given repair-depot system reliability (RDSR), STAT-values are important for scheduling RST. T his paper assumes that repair time is a random variable and, consequently, DRCT is a random variable. As shown in Linton, et al, (1995), STAT is the z ero of a nonlinear, non-polynomial function of DRCT; thus, STAT is also a r andom variable, and determining the distribution of STAT is a stochastic ro ot-finding problem. For n = 1 and s greater than or equal to 0, numerical a nalysis and probability theory are used to find the Cdf and pdf of STAT in terms of any repair time pdf Using the pdf's for STAT and repair time, expr essions are derived for E{LRST} for a NFU, q = Pr {(repair time + c) < STAT}, c = 0 and c =E{LRST}. When the repair time Cdf is exponential or 2-Erlang, numerical values are o btained for q and E(LRST), and it is shown how these values may be used by depot management to schedule RST for a NFU.