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May 2019 Hierarchical modelling of power law processes for the analysis of repairable systems with different truncation times: An empirical Bayes approach
Rodrigo Citton P. dos Reis, Enrico A. Colosimo, Gustavo L. Gilardoni
Braz. J. Probab. Stat. 33(2): 374-396 (May 2019). DOI: 10.1214/18-BJPS393

Abstract

In the data analysis from multiple repairable systems, it is usual to observe both different truncation times and heterogeneity among the systems. Among other reasons, the latter is caused by different manufacturing lines and maintenance teams of the systems. In this paper, a hierarchical model is proposed for the statistical analysis of multiple repairable systems under different truncation times. A reparameterization of the power law process is proposed in order to obtain a quasi-conjugate bayesian analysis. An empirical Bayes approach is used to estimate model hyperparameters. The uncertainty in the estimate of these quantities are corrected by using a parametric bootstrap approach. The results are illustrated in a real data set of failure times of power transformers from an electric company in Brazil.

Citation

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Rodrigo Citton P. dos Reis. Enrico A. Colosimo. Gustavo L. Gilardoni. "Hierarchical modelling of power law processes for the analysis of repairable systems with different truncation times: An empirical Bayes approach." Braz. J. Probab. Stat. 33 (2) 374 - 396, May 2019. https://doi.org/10.1214/18-BJPS393

Information

Received: 1 July 2015; Accepted: 1 January 2018; Published: May 2019
First available in Project Euclid: 4 March 2019

zbMATH: 07057452
MathSciNet: MR3919028
Digital Object Identifier: 10.1214/18-BJPS393

Keywords: Bootstrap correction , maximum a posterior density , minimal repair , multiple repairable systems , rejection sampling , reliability

Rights: Copyright © 2019 Brazilian Statistical Association

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Vol.33 • No. 2 • May 2019
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