A delay-time-based inspection model for parallel systems

Abstract

The delay-time concept has been extensively applied in the field of maintenance, especially for determining the optimal inspection or maintenance interval. It defines a two-stage system failure process: the time from new to an initial defect, known as the normal stage, and the time from this defective point to failure, known as the delay-time stage. Previous works using the delay-time concept have mainly focused on single-component systems and multi-component systems with a series configuration. However, parallel systems also exist in reality, but most existing models for parallel systems use either a single-stage time-to-failure process or a Markov chain to describe the failure mechanism. In this article, we propose a new delay-time-based inspection model for a n-component parallel system and study the optimal inspection interval that minimizes the long-term expected cost per unit time. Two maintenance policies are considered, depending on whether the defective/failed components identified are replaced immediately or not. Numerical examples are presented to show the applicability of the model.