Modeling of the optimal multiple inspection policy based on a three-stage failure process.

In line with the fact that major inspections and minor inspections are usually adopted together for system inspection in engineering practice, this paper proposes a multiple inspection policy model based on a three-stage failure process. The concept of the three-stage failure process divides the system lifetime into three stages, that is, normal stage, minor defective stage and severe defective stage. With the consideration of all the possible scenarios for failure renewal, minor inspection renewal and major inspection renewal, a multiple inspection policy model is presented for single-unit systems using the renewal reward theory. The objective of the model is to minimize the long-run expected cost per unit time, with the minor and major inspection intervals as the decision variables. In order to illustrate the applicability of the multiple inspection policy, a single inspection policy counterpart which includes only major inspections is also developed for the purpose of comparison. The threshold value for the minor inspection cost which makes the multiple inspection more favorable than the single inspection policy is studied. Numerical examples are presented and the results show that the multiple inspection policy is better than the single inspection policy when the cost of minor inspection is smaller than the threshold level and other parameters are fixed. [ABSTRACT FROM AUTHOR]