WITHDRAWN: Nonparametric Bayes Estimation of Reliability of a Coherent System

• Activity Number: 566
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Risk Analysis
• Author(s): A.K.M. Rahman and Edsel A. Pena
• Companies: University of South Carolina and University of South Carolina
• Keywords: Partition based Dirichlet prior ; Nonparametric prior ; System Reliability ; Coherent system ; Nonparametric Bayes

Abstract

Simultaneous estimation of system and components reliability is considered when independent partition-based Dirichlet(PBD) prior is assigned on components distribution. Assume n identical system each with K independent components are in the study with random monitoring time. With an autopsy model random observables are right-censored system and component lifetimes. In our nonparametric Bayesian approach we assign independent PBD prior on each component distribution F_j, j=1,2, ..., K and derive nonparametric Bayes estimator of component reliability function bar(F_j) = 1-F_j and system reliability function by bar{F}_{phi}(t) = h_{phi}(bar{F}_1(t), bar{F}_1(t), ... ,bar{F}_K(t)), where 'phi' is the structure function of the system. The product-limit (PL) type estimator of system reliability presented in Doss et al. (Annals of Statistics, 89) is a special case of our estimator, obtained by letting precision of prior measure to be zero. Through simulation studies, we demonstrate that proposed estimator has smaller root-mean-squared errors and smoother than Pl-type estimators and robust in the sense of mis-specification of the prior measure.