“…Since Abdel-Hameed (1975) first proposed to use gamma process as a model for deterioration occurring randomly in time, a great number of maintenance models based on gamma process have been introduced and studied in the literature, which include time-based and condition-based preventive maintenance (see Berenguer, Grall, Dieulle, & Roussignol, 2003;Castro, Barros, & Grall, 2011;Huynh, Barros, Berenguer, & Castro, 2011;Huynh, Castro, Barros, & Berenguer, 2012;Noortwijk, 2009;Pandey & Yuan, 2006, for a review). A common assumption made in the maintenance models based on gamma process is that the maintenance actions can restore the system to the as good as new state, i.e., the maintenance is perfect.…”