An SMDP approach to optimal repair/replacement decisions for systems experiencing imperfect repairs

Abstract

Considers a system (machine) that is subject to failure (breakdown). Two characterizations are presented. In the first characterization, the state of the system is described by the real age of the machine and the number of failures incurred to date. In the second characterization, the state of the system is described by the real age of the machine and the virtual age of the machine. In either characterization, upon failure, the unit may undergo a repair which can partially reset the failure intensity of the unit. The degree of reset assumed by the repair is a function of the characterization utilized. The other alternative, at a failure, is to conduct a major overhaul that serves to refresh the failure intensity of the unit. General cost structures, depending upon (real age, number of failures) in characterization one or (real age, virtual age) in characterization two are permitted. The decision, on failure to repair or renew is formulated as a discrete semi‐Markov Decision process. Optimal decisions are of the threshold type. The threshold rules depend upon the characterization.