“…The objective of these models is to determine the states for which the unit is replaced in order to gain the minimum expected maintenance cost. The other type is to model the system deterioration with the application of renewal models (Barbera et al, 1996(Barbera et al, , 1999Bérenguer et al, 2000;Castanier et al, 2001Castanier et al, , 2005Chu et al, 1998;Dieulle et al, 2003;Grall et al, 2002a,b;Park, 1998;Pellegrin, 1992;Wang, 2003) ith deterioration level X f;j deterioration to failure of the unit j corresponding to the current life cycle X f deterioration to failure, i.e. the deterioration level just when unit failure occurs X i f ith deterioration levels just when failure occurs, i ¼ 1; 2; .…”