An inspection policy for a deteriorating single-unit system characterized by a delay-time model

This paper develops a method for determining the discrete time points of inspection for a deteriorating system which is under condition-based maintenance. The system is regarded as a single component unit, and it has the following states: a normal state, a symptom state and a failed state. A delay-time model is utilized in order to describe the transition of the states. The transition time from a normal state to a symptom state and the transition time from a symptom state to a failed state are assumed to obey independent and identically distributed probability density functions respectively. Two types of probabilities with respect to inspections are considered: failed-dangerous (FD) probability or type I error that a system is wrongly diagnosed as in a normal state when the system is actually in a symptom state and failed-safe (FS) probability or type II error that a system is wrongly diagnosed as in a symptom state when the system is actually in a normal state. The determination method is formulated to minimize the long-run average cost per unit time with a constraint on inspection time. The nature and sensitivity of the proposed method is investigated under varying FD and FS probabilities and coefficients of variation.