An alternative competing risk model to the Weibull distribution for modelling aging in lifetime data analysis

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.

[1]  K. Chanda.  A NOTE ON THE CONSISTENCY AND MAXIMA OF THE ROOTS OF LIKELIHOOD EQUATIONS , 1954 .

[2]  Nozer D. Singpurwalla,et al.  Bayesian Reliability Demonstration. Phase 1. Data for the A Priori Distribution , 1970 .

[3]  T. S. Sheffield,et al.  Bayesian Reliability Demonstration: Phase II. Development of a Priori Distribution. , 1971 .

[4]  I. Gertsbakh,et al.  Maximum Likelihood Estimation in a Mininum-Type Model with Exponential and Weibull Failure Modes , 1980 .

[5]  Pasquale Erto.  New Practical Bayes Estimators for the 2-Parameter Weibull Distribution , 1982, IEEE Transactions on Reliability.

[6]  Jerald F. Lawless,et al.  Statistical Models and Methods for Lifetime Data. , 1983 .

[7]  Ralph B. D'Agostino,et al.  Goodness-of-Fit-Techniques , 2020 .

[8]  W. Wong,et al.  The calculation of posterior distributions by data augmentation , 1987 .

[9]  Thorn J. Hodgson,et al.  Maximum likelihood analysis of component reliability using masked system life-test data , 1988 .

[10]  Christian Gourieroux,et al.  Statistique et modèles économétriques , 1989 .

[11]  Martin Abba Tanner,et al.  Tools for Statistical Inference: Observed Data and Data Augmentation Methods , 1993 .

[12]  James O. Berger,et al.  Bayesian Analysis for the Poly-Weibull Distribution , 1993 .

[13]  James O. Berger,et al.  Bayesian sequential reliability for Weibull and related distributions , 1994 .

[14]  Els Goetghebeur,et al.  Analysis of competing risks survival data when some failure types are missing , 1995 .

[15]  G. McLachlan,et al.  The EM algorithm and extensions , 1996 .

[16]  W. Nelson.  Statistical Methods for Reliability Data , 1998 .

[17]  W. Q. Meeker,et al.  A failure-time model for infant-mortality and wearout failure modes , 1999 .

[18]  Henri Bertholon,et al.  Une modélisation du vieillissement , 2001 .

[19]  Emmanuel Yashchin,et al.  Parametric Modeling for Survival with Competing Risks and Masked Failure Causes , 2002, Lifetime data analysis.

[20]  J. Lawless.  Statistical Models and Methods for Lifetime Data , 2002 .

[21]  Sanjib Basu,et al.  Bayesian analysis of competing risks with partially masked cause of failure , 2003 .

[22]  Gordon Johnston,et al.  Statistical Models and Methods for Lifetime Data , 2003, Technometrics.

[23]  Jean-Michel Marin,et al.  Convergence of Adaptive Sampling Schemes , 2004 .

[24]  O. Cappé,et al.  Population Monte Carlo , 2004 .

[25]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[26]  Radu V. Craiu,et al.  Inference based on the EM algorithm for the competing risks model with masked causes of failure , 2004 .

[27]  W. J. Padgett,et al.  Analysis of strength distributions of multi-modal failures using the EM algorithm , 2006 .

[28]  Adrian E. Raftery,et al.  Computing Normalizing Constants for Finite Mixture Models via Incremental Mixture Importance Sampling (IMIS) , 2006 .

[29]  Jean-Michel Marin,et al.  Iterated importance sampling in missing data problems , 2006, Comput. Stat. Data Anal..