Using system reliability to determine supportability turnaround time at a repair depot

Abstract

This paper uses an expression for system reliability at a repair depot to construct a nonlinear, nonpolynomial function which is amenable to numerical analysis and has a zero equal to the supportability turnaround time (STAT) for a failed unit. System reliability is in terms of the constant failure rate for all units, number of spares on-hand at the time a unit fails, and projected repair completion dates for up to four unrepaired units. In this context, STAT represents the longest repair time (for a failed unit) which assures a given reliability level; system reliability is the probability that spares are ready to replace failed units during the STAT period. The ability to calculate STAT-values is important for two reasons: (1) subtraction of the repair time for a failed unit from its STAT-value yields the latest repair start-time (for this unit) which assures a desired reliability, and (2) the earlier the latest repair start-time, the higher the priority for starting the repair of this unit. Theorems show the location of STAT with respect to the list of repair completion dates, and form the foundation of the root-finding-based algorithm for computing STAT-values. Numerical examples illustrate the algorithm.