An alternative competing risk model to the Weibull distribution for modelling aging in lifetime data analysis
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A simple competing risk distribution as a possible alternative to the Weibull distribution in lifetime analysis is proposed. This distribution corresponds to the minimum between exponential and Weibull distributions. Our motivation is to take account of both accidental and aging failures in lifetime data analysis. First, the main characteristics of this distribution are presented. Then, the estimation of its parameters are considered through maximum likelihood and Bayesian inference. In particular, the existence of a unique consistent root of the likelihood equations is proved. Decision tests to choose between an exponential, Weibull and this competing risk distribution are presented. And this alternative model is compared to the Weibull model from numerical experiments on both real and simulated data sets, especially in an industrial context.
KeywordsFailure time distribution Aging Weibull distribution Accidental failure Competing risk model EM algorithm Bayesian inference Importance sampling Likelihood ratio test
We warmly thank the Associate Editor and the reviewers for their numerous suggestions and corrections which greatly help to improve the presentation of the paper.
- Bacha M, Celeux G, Idée E, Lannoy A, Vasseur D (1998) Estimation de modèles de durées de vie fortement censurées”. Eyrolles, ParisGoogle Scholar
- Bertholon H (2001) Une modélisation du vieillissement, PhD Thesis, Université Joseph Fourier, GrenobleGoogle Scholar
- Douc R, Guillin A, Marin JM, Robert CP (2005) Convergence of adaptive sampling schemes. Research Paper RR-5485, INRIA Futurs, FebruaryGoogle Scholar
- Gourieroux Ch, Monfort A (1996) Statistique et modèles économétriques. Economica, ParisGoogle Scholar
- INSEE (2001) National French Institute for Statistics and Economic Studies, 195, rue de Bercy—Tour Gamma A—75582 Paris cedex 12, France, http://www.insee.fr.Google Scholar
- Lannoy A, Procaccia H (2001) L’utilisation du jugement d’expert en sûreté de fonctionnement, éditions Tec&Doc, ParisGoogle Scholar
- Park C, Padgett WJ (2004) Analysis of strength distributions of multi-modal failures using the EM algorithm. Technical report No. 220, Department of Statistics, University of South Carolina,Google Scholar
- Schafer RE (1969) Bayesian reliability demonstration, phase I–data for the a priori distribution, RADC-TR-69-389, Rome Air Development CenterGoogle Scholar
- Schafer RE, Sheffield TS (1971) Bayesian reliability demonstration, phase II—development of a prior distribution, RADC-TR-71-139, Rome Air Development CenterGoogle Scholar
- Steele R, Raftery AE, Emond M (2003) Computing normalizing constants for finite mixture models via incremental mixture importance sampling (IMIS). Technical Report no. 436, Department of Statistics, University of WashingtonGoogle Scholar
- Tanner MA (1991) Tools for statistical inference, observed data and data augmentation methods, Lectures notes in statistics. Springer-Verlag, New YorkGoogle Scholar