Bayesian Analysis of Masked Series System Lifetime Data

The problem of analyzing series system lifetime data with masked or partial information on cause of failure is recent, compared to that of the standard competing risks model. A generic Gibbs sampling scheme is developed in this article towards a Bayesian analysis for a general parametric competing risks model with masked cause of failure data. The masking probabilities are not subjected to the symmetry assumption and independent Dirichlet priors are used to marginalize these nuisance parameters. The developed methodology is illustrated for the case where the components of a series system have independent log-Normal life distributions by employing independent Normal-Gamma priors for these component lifetime parameters. The Gibbs sampling scheme developed for the required analysis can also be used to provide a Bayesian analysis of data arising from the conventional competing risks model of independent log-Normals, which interestingly has so far remained by and large neglected in the literature. The developed methodology is deployed to analyze a masked lifetime data of PS/2 computer systems.

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

[2]  Gregg E. Dinse,et al.  Nonparametric prevalence and mortality estimators for animal experiments with incomplete cause-of-death data , 1986 .

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

[4]  James O. Berger,et al.  Statistical Decision Theory and Bayesian Analysis, Second Edition , 1985 .

[5]  Emmanuel Yashchin,et al.  Inference about defects in the presence of masking , 1996 .

[6]  Chiranjit Mukhopadhyay,et al.  Maximum likelihood analysis of masked series system lifetime data , 2006 .

[7]  I Guttman,et al.  Dependent masking and system life data analysis: Bayesian inference for two-component systems , 1995, Lifetime data analysis.

[8]  L. Kuo,et al.  Bayesian reliability modeling for masked system lifetime data , 2000 .

[9]  Chiranjit Mukhopadhyay,et al.  Bayesian analysis for masked system failure data using non-identical Weibull models , 1999 .

[10]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

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

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

[13]  Frank M. Guess,et al.  Estimating system and component reliabilities under partial information on cause of failure , 1991 .

[14]  Masami Miyakawa,et al.  Analysis of Incomplete Data in Competing Risks Model , 1984, IEEE Transactions on Reliability.

[15]  Frank M. Guess,et al.  System life data analysis with dependent partial knowledge on the exact cause of system failure , 1994 .

[16]  Asit P. Basu,et al.  Bayesian analysis of incomplete time and cause of failure data , 1997 .

[17]  Emmanuel Yashchin,et al.  Survival with competing risks and masked causes of failures , 1998 .

[18]  Adrian F. M. Smith,et al.  Bayesian computation via the gibbs sampler and related markov chain monte carlo methods (with discus , 1993 .

[19]  G. Dinse,et al.  Nonparametric estimation for partially-complete time and type of failure data. , 1982, Biometrics.

[20]  Frank M. Guess,et al.  Bayesian inference for masked system lifetime data , 1995 .