Journal of Statistical Theory and Applications

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Volume 20, Issue 1, March 2021, Pages 149 - 163

Bayesian Estimation of System Reliability Models Using Monte-Carlo Technique of Simulation

Authors
Kirti Arekar1, *, Rinku Jain1, Surender Kumar2
1Associate Professor, K.J. Somaiya Institute of Management Studies and Research, Mumbai, India
2Adjunt Faculty, K.J. Somaiya Institute of Management Studies and Research, Mumbai, India
*Corresponding author. Email: kirtiarekar@somaiya.edu; deshmukh_k123@yahoo.com
Corresponding Author
Kirti Arekar
Received 15 April 2019, Accepted 12 November 2020, Available Online 8 February 2021.
DOI
10.2991/jsta.d.210201.001How to use a DOI?
Keywords
Bayesian estimation; Bayes Estimator; Reliability; Monte-Carlo simulation
Abstract

This paper discusses the problem of how Monte-Carlo simulation method is deal with Bayesian estimation of reliability of system of n s-independent two-state component. Time-to-failure for each component is assumed to have Weibull distribution with different parameters for each component. The shape parameter for each component is assumed to be known with the scale parameter distributed with a priori Rayleigh distribution with known parameters. Monte-Carlo simulation is used to generate the random deviates for the scale parameters and replicates for time-to-failure for each combination of scale parameters values are generated. Reliability is estimated as a function of time. Further, for the Bayes estimation of reliability we assume Poisson distribution with a priori time-shifted Rayleigh distribution. Finally, the robustness in the Bayesian estimation problem relative to changes in the assigned priori distribution is considered. We approximate the Bayes estimator of the reliability. The Bayes risk with respect to the priori time-shifted beta distribution is considered and at last approximate robustness of the Bayes estimator of reliability is examined with respect to the uniform priori. We have compared the maximum likelihood estimator of reliability with the Bayes estimator with prior uniform distribution. Finally, the method is illustrated by considering the illustrative example of vehicle system.

Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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<Previous Article In Issue
Journal
Journal of Statistical Theory and Applications
Volume-Issue
20 - 1
Pages
149 - 163
Publication Date
2021/02/08
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
10.2991/jsta.d.210201.001How to use a DOI?
Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Kirti Arekar
AU  - Rinku Jain
AU  - Surender Kumar
PY  - 2021
DA  - 2021/02/08
TI  - Bayesian Estimation of System Reliability Models Using Monte-Carlo Technique of Simulation
JO  - Journal of Statistical Theory and Applications
SP  - 149
EP  - 163
VL  - 20
IS  - 1
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.210201.001
DO  - 10.2991/jsta.d.210201.001
ID  - Arekar2021
ER  -