A replacement model with general age-dependent failure rates
Models for a repairable system [cf. \textit{W. Stadje} and \textit{D. Zuckerman}, Adv. Appl. Probab. 22, No. 3, 641-656 (1990; Zbl 0704.60085)] are studied using techniques from the theories of dynamic programming, optimal stopping, point processes, and Markov processes. Both the operating and repair times are time-dependent random variables, and optimal replacement rules are found for the finite horizon case with and without discounting, with corollaries that it is never optimal to replace in the middle of a repair period for repair-time distributions which are NBUE (new better than used in expectation). General monotonicity properties of the value functions are derived, and the optimal replacement times for the infinite horizon case are obtained from the finite horizon case by taking limits.
scientific article; zbMATH DE number 1040414
scientific article