Modelling Recurrent Events for Repairable Systems Under Worse Than Old Assumption

Génia Babykina , Vincent Couallier (1)

1 IMB - Institut de Mathématiques de Bordeaux

The objective of the work is to model the failure process of a repairable system under "worse than old", or harmful repairs, assumption. The proposed model is founded on the counting process probabilistic approach and interprets harmful repairs as the accumulation of failures on the same system. Increase in the conditional intensity is rather induced by the number of previous repair actions than by time contrarily to virtual age models. The LEYP model is defined and some comparison with existing imperfect repair models is given. The explicit form of likelihood function is provided. A covariate-dependent model is defined in order to take the effect of internal or external factors, which may be constant or time dependent, into account. After a description of the estimation procedure for left-truncated and right-censored data using a multiple systems data set, we provide some useful formulae for prediction of the number of failures in a future period. An application to data from the water distribution system of the city of Oslo (Norway) is given.

Mots clés: counting processes; repairable systems; recurrent events; time-dependent covariates

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Génia Babykina, Vincent Couallier. Modelling Recurrent Events for Repairable Systems Under Worse Than Old Assumption. Nikulin, M. S. and Limnios, N. and Balakrishnan, N. and Kahle, W. and Huber-Carol, C. Advances in Degradation Modeling, Birkhäuser Boston, pp 339-354, 2010, Statistics for Industry and Technology, 978-0-8176-4923-4. ⟨10.1007/978-0-8176-4924-1_22⟩. ⟨hal-00968110⟩