Bayesian estimation of Weibull mixture in heavily censored data setting

Florence Ducros (1) , Patrick Pamphile (2, 3)

1 NEXTER Systems
2 LMO - Laboratoire de Mathématiques d'Orsay
3 SELECT - Model selection in statistical learning

Lifetime data collected from a fleet of vehicles or, more broadly, park of systems are generally non-homogeneous and heavily censored. Indeed, system lifetime can be affected by the variability of production conditions and usage conditions. Most of the time, this variability is unobserved, but has to be taken into account for reliability or warranty cost analysis. This research proposes a two-component Weibull mixture model for modelling unobserved heterogeneity in in heavily censored lifetime data collection. Performance of classical estimation methods (maximum of likelihood, EM, full Bayes and MCMC) are significantly reduced due to the high number of parameters and the heavy censoring. Therefore , a Bayesian bootstrap method, called Bayesian Restauration Maximisation, is used. Sampling from the posterior distribution is obtained thanks to an importance sampling technique. Simulation results showed that, even with heavy censoring, BRM is effective both in term of estimates precision and computation times. The prior elicitation, sensibility analysis and comparaisons with EM are discussed. Finally, a real data set is analyzed to illustrate the application of the method.

Mots clés: Bayesian estimation; Warranty cost; Reliability analysis; Non-homogeneous data; Weibull mixture; Heavily censored data

Domaines: Applications [stat.AP]; Méthodologie [stat.ME]

Florence Ducros, Patrick Pamphile. Bayesian estimation of Weibull mixture in heavily censored data setting. Reliability Engineering and System Safety, 2018. ⟨hal-01645618⟩