Exact Results on the Statistically Expected Total Cost and Optimal Solutions for Extended Periodic Imperfect Preventive Maintenance

Sheu and Chang (IEEE Trans. Rel., vol. 58, no. 2, pp. 397-404, 2009) presented an interesting extended periodic imperfect preventive maintenance (EPIPM) model for a system with age-dependent failure type. Many cases studied previously are special cases of the EPIPM model. In the Errata (IEEE Trans. Rel., vol. 60, no. 2, 2011), Sheu and Chang showed that the proposed effective age and the proposed hazard rate function after the PM are incorrect. In this paper, based on the correct failure characteristics (effective age and hazard rate function after PM), the correct
s
-expected total cost per unit time for the EPIPM model is presented. By assigning three types of failure characteristics for the EPIPM model, we analyse and compare the corresponding
s
-expected total costs per unit time. We find that the
s
-expected total cost per unit time developed by Sheu and Chang (IEEE Trans. Rel., vol. 58, no. 2, pp. 397-404, 2009) is only one upper bound of the exact
s
-expected total cost per unit time. In addition, we also give some results on the existence of the optimal solution for the exact
s
-expected total cost.