Assessing the effect of repair delays on a repairable system

Abstract

Repair delays are common in systems where failures are not self-revealed or in mission-critical systems where repairs cannot be conducted during a mission. The presence of repair delays may significantly affect the failure behavior of a system, but its impact has been largely overlooked in the literature. In this article, we propose a flexible intensity-based model for repairable systems subject to repair delays. Statistical inference of the model is discussed. In the presence of repair delays, the exact failure times are typically unavailable and the failures are only known to occur at times within intervals with known lower and upper bounds. In this case, the likelihood function is complicated. We introduce several efficient numerical integration methods to evaluate the likelihood function and investigate their performance through comprehensive simulations. Goodness-of-fit tests are used to check the adequacy of the baseline rate of occurrence of failures and the effect of repair delays. The proposed methods are demonstrated using maintenance data of a general infusion pump used in a hospital.