Preventive Replacement of a 1-Unit System with a Wearout State

This paper is concerned with a 1-unit system with 3 types of states: usual, wearout, and failure; the hazard rate is constant in the usual state and is monotonically increasing and unbounded in the wearout state. In order to deal with this system in detail, we introduce two models: model 1 in which the period of normal operation is fixed and model 2 in which it is a random variable with a negative exponential distribution function. The models have different preventive replacement policies based on both age and state. Moreover we give the conditions under which these policies are effective.