A fast algorithm for repair-depot reliability-evaluation

The repair-depot (where failed items are replaced with spares and scheduled for repair) system-reliability (RDSR) is the probability that spares are immediately available to replace failed units during the time period of interest, and it is calculated in terms of the constant failure rate for parts under consideration, the number of spare units on-hand (s), and projected repair completion dates for (n-1) units in the repair process, n⩾2. Linton et al. (1995) show an expression for RDSR in terms of n nested sums, where the upper limit of each sum is a function of s. This paper derives a restructured expression (LKYH algorithm) for computing RDSR, and shows that the nested-sum form for RDSR uses O(sⁿ) mathematical operations, while LKYH requires only O(s) mathematical operations. Numerical examples illustrate the increase in efficiency of LKYH; e.g., when n=s=10, the execution time for computing RDSR on a 486/66-computer is reduced from 198 seconds for the multiple-sum form to less than 1 second for LKYH