Statistical inference for imperfect maintenance models with missing data

Virtual age, is it real? ‐ Discussing virtual age in reliability context

“…A recent work by Mercier and Castro 13 presents rigorous stochastic comparisons between the age reduction models with degradation reduction models (see below). A survey on virtual age models based on (1) and its generalizations (Kijima‐type modeling) can be found in Tanwar et al 14 See also Dijoux et al 15 and Nguyen et al 16 and references therein, where a comprehensive analysis of the literature on the subject is performed. Lindqvist 17 have generalized the univariate virtual age/imperfect repair concept for repairable multicomponent systems.…”

“…On the other hand, although not practically justified in the sense defined above, this black‐box reasoning can be effectively used, in principle, for fitting the real imperfect repair data, which is done in numerous publication (see Levitin and Lisniansky, 20 Dijoux et al, 15 de Toledo et al, 21 Liu et al, 10 to name a few). In fact, this is the case for many statistical applications when the model itself does not necessarily follow the real, for example, degradation processes which it models.…”

Virtual age models with time-dependent covariates: A framework for simulation, parametric inference and quality of estimation

“…For these models, Chauvel et al [5] proposed goodness-of-fit tests wih a parametric bootstrap approach. Other models were designed, generally with an estimation procedure, for example by Dauxois and Maalouf [6], Dauxois et al [7], Dijoux et al [8], Doyen et al [9], and Peng et al [10]. Some models also include preventive maintenances, as those exposed by Peng et al [11], Said and Taghipour [12] and Salles et al [13].…”

Discussion of “Virtual age, is it real?”

“…The virtual age modeling is particularly useful for fitting the real repair data and has been widely used in reliability practice. See, for example, Dorado et al, 4 Dijoux et al, 5 and references therein for statistical issues on this subject.…”