State-age-dependent maintenance policies for deteriorating systems with Erlang sojourn time distributions

https://doi.org/10.1016/S0951-8320(97)00049-5Get rights and content

Abstract

This paper investigates state-age-dependent maintenance policies for multistate deteriorating systems with Erlang sojourn time distributions. Since Erlang distributions are serial combinations of exponential phases, the deteriorating process can be modeled by a multi-phase Markovian model and hence easily analyzed. Based on the Markovian model, the optimal phase-dependent inspection and replacement policy can be obtained by using a policy improvement algorithm. However, since phases are fictitious and can not be identified by inspections, two procedures are developed to construct state-age-dependent policies based on the optimal phase-dependent policy. The properties of the constructed state-age-dependent policies are further investigated and the performance of the policy is evaluated through a numerical example.

References (17)

  • J.A.M. Hontelez et al.

    Optimum condition-based maintenance policies for deteriorating systems with partial information

    Reliability Engineering and System Safety

    (1996)
  • R. Dekker

    Applications of maintenance optimization models: a review and analysis

    Reliability Engineering and System Safety

    (1996)
  • C.T. Lam et al.

    Optimal maintenance policies for deteriorating systems under various maintenance strategies

    IEEE Transactions on Reliability

    (1994)
  • R.E. Barlow et al.

    Mathematical Theory of Reliability

    (1965)
  • J.J. McCall

    Maintenance policies for stochastically failing equipment: a survey

    Management Science

    (1965)
  • W.P. Pierskalla et al.

    A survey of maintenance models: the control and surveillance of deteriorating systems

    Naval Research Logistics Quarterly

    (1976)
  • Y.S. Sherif et al.

    Optimal maintenance models for systems subject to failure — a review

    Naval Research Logistics Quarterly

    (1981)
  • C. Valdez-Flores et al.

    A survey of preventive maintenance models for stochastically deteriorating single-unit systems

    Naval Research Logistics

    (1989)
There are more references available in the full text version of this article.

Cited by (42)

  • Cost effective scheduling of imperfect inspections in systems with hidden failures and rescue possibility

    2019, Applied Mathematical Modelling
    Citation Excerpt :

    Refer to [6] for a survey explaining and comparing different models. Examples include periodic inspections or preventive maintenance models [3,7–10], age-dependent models [11–13], condition-based inspection models [14–16], predictive models [17–19], opportunistic policies [1,20–23], preparedness models [24], reference-time based models [25,26], risk-based inspections [27–29], etc. Based on time span considered, inspection policies have been investigated for systems over infinite and finite time horizons while the finite one is more practical as the mission time or operation time of real-world system units is usually limited [30,31].

  • An integrated framework for online diagnostic and prognostic health monitoring using a multistate deterioration process

    2014, Reliability Engineering and System Safety
    Citation Excerpt :

    The second limitation of current studies is the lack of model selection approaches. In other words, in most work in the literature, it is assumed that the structure of the multistate degradation process is already known [15,16]. Here, structure refers to certain elements, such as the number of states, the connectivity between states, the distribution of transitions between states, the stochastic relationship between the actual health states and the condition monitoring data, which together characterize the associated multistate degradation process.

  • Fatigue crack growth estimation by relevance vector machine

    2012, Expert Systems with Applications
    Citation Excerpt :

    Many researchers have focused on the problem of building exhaustive models of deteriorating components and structures to implement model-based prognostic tools. Markov and semi-Markov models have been widely exploited for achieving analytical results (Baruah & Chinnam, 2005; Bérenguer, Grall, & Castanier, 2000; Dong & He, 2007; Grall, Bérenguer, & Chu, 1998; Hontelez, Burger, & Wijnmalen, 1996; Kopnov, 1999; Lam & Yeh, 1994; Samanta, Vesely, Hsu, & Subudly, 1991; Yeh, 1997). On the basis of these models, several approaches have been proposed to analyze reliability-based and condition-based maintenance policies (Castanier, Bérenguer, & Grall, 2002; Chen & Trivedi, 2005; Pulkkinen & Uryas’ev, 1992; Vlok, Coetzee, Banjevic, Jardine, & Makis, 2002).

  • Optimal integrated process control and maintenance under general deterioration

    2012, Reliability Engineering and System Safety
    Citation Excerpt :

    In this context Kao [12], So [13], Lam and Yeh [14], Moustafa et al. [15] and Kim and Makis [16] derive optimal state-dependent or state-age-dependent preventive maintenance policies but they assume that the actual operating state is continuously and accurately known. Yeh [17,18] and Chen and Trivedi [19] expand the previous semi-Markovian models assuming intermittent inspections and derive the optimal inspection frequency as well, but they also assume that inspections provide perfect information about the process state. More general non-Markovian maintenance models under continuous and accurate monitoring have been presented by Al-Ali and Murari [20], Murthy and Iskadar [21], Su and Chang [22] and Panagiotidou and Tagaras [23,24].

View all citing articles on Scopus
View full text