An inspection and replacement model based on a three-stage failure process

This paper proposes an inspection and replacement model based on a three-stage failure process for a single-unit system to minimize the expected cost per unit time. The models using the two-stage failure process for optimizing the inspection interval of the system have been addressed by many others. However, a three-stage failure process provides more modeling options and is closer to reality since a binary description of the system's state is restrictive. It is assumed that the system needs to be repaired immediately in case in a severe defective stage being identified at an inspection or at a failure, and replaced once it reaches a certain age, however, two different kinds of maintenance decisions are made if the system is identified to be in a minor defective stage at an inspection. Both repair and replacement renew the system. Various cost models are studied under different maintenance policies and a numerical example is presented to illustrate the applicability of the model.