Bayesian Analysis of Masked Series System Lifetime Data

Abstract

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.

Keywords:

• Censoring
• Competing risks
• Dirichlet distribution
• Gibbs sampling
• log-Normal distribution
• Masking probabilities
• Normal-gamma prior
• Reliability

Mathematics Subject Classification:

• 62F15
• 62N05
• 62P30

Acknowledgment

The authors would like to thank an anonymous referee whose suggestions helped greatly improve the scope of the revised version of the article.

Notes

∗1: Mother Board; 2: Disc Drives; 3: Power Supply.