Generalized models of repairable systems: A survey via stochastic processes formalism

Abstract

In this article, we survey the developments in the generalised models of repairable systems reliability during 1990s, particularly the last five years. In this field, we notice the sharp fundamental problem that voluminous complex models were developed but there is an absence of sufficient data of interest for justifying the success in tackling the real engineering problems. Instead of following the myth of using simple models to face the complex reality, we select and review some practical models, particularly the stochastic processes behind them. The Models in three quick growth areas: age models, condition monitoring technique related models, say, proportional intensity and their extensions, and shock and wearing models, including the delay-time models are reviewed. With the belief that only those stochastic processes reflecting the instinct nature of the actual physical processes of repairable systems, without excessive assumptions, may have a better chance to meet the demands of engineers and managers.

Statistical inference for imperfect maintenance models with missing data

“…Large classes of virtual age models have been presented in [16,22,25]. The ABAO and the AGAN cases correspond to = A T i i and A i ¼0, respectively.…”

“…The models used in this section are the imperfect maintenance models presented in Section 5: ARA 1 , ∞ ARA and Brown-Proschan. To compare the performance of different modeling schemes (with and without considering initial age), we propose three approaches, each associated with an estimation method: Approach 1 considers that the initial age is different from zero and uses the likelihood functions developed in previous section: (22) It is worth to notice that the assumption used by Approach 3 is hardly available in practice. It represents however an ideal case of the problem under consideration, and therefore serves as a reference to evaluate the performance of methods 1 and 2.…”

Imperfect preventive maintenance for numerical control machine tools with log-linear virtual age process

“…The long-run average cost with N cycles is [12] (16) where c m , c p and c r denote the cost of a minimal repair, a PM action and system replacement, respectively.…”

“…Another important imperfect maintenance model is virtual age model proposed by KIJIMA et al [10−11]. GUO et al [12] generalized this virtual age concept to virtual age process. Based on the failure intensity reduction or virtual age, DOYEN and GAUDOIN [13] studied the classes of imperfect repair models.…”

A Delay-Time Model with Imperfect Inspections for Multi-Unit Systems / Model Opóźnień Czasowych Z Nieperfekcyjną Diagnozą Stanu Systemu Dla Systemów Wieloelementowych

“…[24,25,30]. A literature review, in which delay-time models are investigated along with other PM models are given in [20,21,22,29,32,35,36]. The state of art works, dedicated strictly to DT modelling are given in [1,3,6,7,8,11,12,28,30,33,37].…”