Updated the 1/03/16

Imperfect maintenance models

A major issue for industrial systems is the joint management of ageing and maintenance. An efficient maintenance and a controlled ageing allow the extension of the operating life of equipment. There are several kinds of maintenance. Corrective maintenance (CM), also called repair, is carried out after a failure and intends to put the system into a state in which it can perform its function again. Preventive maintenance (PM) is carried out when the system is operating and intends to slow down the wear process and reduce the frequency of occurrence of system failures. PM can be planned or condition-based. Condition-based PM occur at unscheduled times, which are determined according to the results of inspections and degradation or operation controls. PM is planned when it is done at scheduled times, according to a PM policy.

The basic assumptions on maintenance efficiency are known as minimal maintenance or As Bad As Old (ABAO) and perfect maintenance or As Good As New (AGAN). In the ABAO case, each maintenance leaves the system in the state it was before maintenance. In the AGAN case, each maintenance is perfect and leaves the system as if it were new. When only CM are considered the corresponding models are respectively the Non Homogeneous Poisson Process (NHPP) and the Renewal Process (RP). It is well known that reality is between these two extreme cases: standard maintenance reduces failure intensity but does not leave the system as good as new. This is known as imperfect maintenance.

Many imperfect maintenance models have been proposed. Among them the virtual age models proposed by Kijima [2] assumed that maintenance rejuvenates the system. Another widely used model is the Brown-Proschan (BP) model [1], in which system state after maintenance is assumed to be AGAN with probability p and ABAO with probability (1-p).

My research interests are principally based on that context:
  • - We propose and study two new classes of imperfect repair models known as Arithmetic Reduction of Age (ARA) models and Arithmetic Reduction of Intensity (ARI) models [3]. For those models I have studied the asymptotic properties of different parametric estimators of the repair efficiency [5].
  • - We propose and study two general frameworks for the simultaneous modeling and assessment of CM and PM actions and ageing. The first framework is dedicated to condition based PM [4], and models are based on competing risks and colored processes. The second framework is dedicated to planned PM [7].
  • - I study the probabilistic and statistical properties of the BP model both for system submitted only to BP CM [6] and jointly to ABAO CM and BP PM at fixed times [8]. For the same model, I have also proposed a semi-parametric estimation method [11]. The originality of those studies is to consider that maintenance BP effects (ABAO or AGAN) are not observed. Thanks to the random effect of BP PM model, it is possible to individually assess the effect of each PM action.
  • - We have also studied the Bayesian analysis of imperfect maintenance models, in the case where only CM actions are considered [9], and we are finalizing a work in which we also consider PM.
  • - Presently, I am working on goodness of fit tests for imperfect maintenance models [13].
  • - I have began a more theoretical work with E. Beutner (Maastricht University) et L. Bordes (LMAP à l’université de Pau et des Pays de l'Adour) on the asymptotic properties of the semi-parametric estimators for ARA models [12].
  • - We also proposed a more applied study about an integrated approach for maintenance efficiency estimation and technical and economic optimization of PM periodicity [10].

  • [1] M. Brown and F. Proschan, Imperfect repair. Journal of Applied Probability 20 (1983), pp. 851-859.
  • [2] M. Kijima, Some results for repairable systems with general repair. Journal of Applied Probability 26 (1989), pp. 89-102.
  • [3] L. Doyen and O. Gaudoin, Classes of imperfect repair models based on reduction of failure intensity or virtual age. Reliability Engineering and System Safety 84 (2004), pp. 45-56.
  • [4] L. Doyen and O. Gaudoin, Imperfect maintenance in a generalized competing risks framework. Journal of Applied Probability 43 (2006), pp. 825-839.
  • [5] L. Doyen, Asymptotic properties of imperfect repair models and estimation of repair efficiency. Naval Research Logistics 57 (2010), pp. 296-307.
  • [6] L. Doyen, Brown-Proschan model when repair effects are unknown. Applied Stochastic Models in Business and Industry 27 (2011), pp. 600-618.
  • [7] L. Doyen and O. Gaudoin, Modelling and assessment of ageing and efficiency of corrective and planned preventive maintenance. IEEE Trans. Reliab. 60 (2011), pp. 759-769.
  • [8] L. Doyen, Reliability analysis and joint assessment of Brown-Proschan preventive maintenance efficiency and intrinsic wear-out 56 (2012), pp. 4433-4449.
  • [9] F. Corset and L. Doyen and O. Gaudoin, Bayesian analysis of ARA imperfect repair models. Commun. Stat.-Theory Methods 41 (2012), pp. 3915-3941.
  • [10] E. Rémy, F. Corset, S. Despréaux, L. Doyen and O. Gaudoin, An example of integrated approach for the technical and economic optimization of maintenance. Reliability Engineering and System Safety 116 (2013), pp. 8-19.
  • [11] L. Doyen, Semi-parametric estimation of Brown-Proschan preventive maintenance effects and intrinsic wear-out. Computational Statistics and Data Analysis 77 (2014) pp. 206-222.
  • [12] E. Beutner, L. Bordes and L. Doyen, Semi-parametric estimation of Brown-Proschan preventive maintenance effects and intrinsic wear-out. The failure of the profile likelihood method for semi-parametric effective age models (submitted 2015) .
  • [13] C. Chauvel, J.Y. Dauxois, L. Doyen and O. Gaudoin, Parametric bootstrap goodness-of-fit tests for imperfect maintenance models (submitted 2015).