Incorrect modeling of the failure process of minimally repaired systems under random conditions: the effect on the maintenance costs

This note investigates on the effect of the incorrect modeling of the failure process of minimally repaired systems that operates under random environmental conditions on the costs of a periodic replacement maintenance. The motivation of this paper is given by a recently published paper, where a wrong formulation of the expected cost for unit time under a periodic replacement policy is obtained. This wrong formulation is due to the incorrect assumption that the intensity function of minimally repaired systems that operate under random conditions has the same functional form as the failure rate of the first failure time. This produced an incorrect optimization of the replacement maintenance. Thus, in this note the conceptual differences between the intensity function and the failure rate of the first failure time are first highlighted. Then, the correct expressions of the expected cost and of the optimal replacement period are provided. Finally, a real application is used to measure how severe can be the economical consequences caused by the incorrect modeling of the failure process.