On Bayesian reliability estimation of a 1-out-of-k load sharing system model of modified Burr-III distribution

This article deals with classical and Bayesian estimation of the parameters of a 1-out-of-k load-sharing parallel system model in which each component’s lifetime follows modified Burr-III distribution. In the classical set up, the maximum likelihood estimates of the load-share parameters, system rel...

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Bibliographic Details
Published in:International journal of system assurance engineering and management 2019-10, Vol.10 (5), p.1052-1081
Main Authors: Ali, Azeem, Dey, Sanku, Ur Rehman, Haseeb, Ali, Zeeshan
Format: Article
Language:English
Subjects:
Bayesian analysis
Bias
Computer simulation
Confidence intervals
Economic models
Engineering
Engineering Economics
Load sharing
Logistics
Marketing
Mathematical models
Maximum likelihood estimates
Maximum likelihood estimators
Organization
Original Article
Parameter estimation
Quality Control
Reliability
Safety and Risk
Service life assessment
Statistical analysis
System reliability
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Summary:This article deals with classical and Bayesian estimation of the parameters of a 1-out-of-k load-sharing parallel system model in which each component’s lifetime follows modified Burr-III distribution. In the classical set up, the maximum likelihood estimates of the load-share parameters, system reliability and hazard rate functions with their bias, standard errors (SEs), average absolute bias (AABias) and width of the confidence interval along with coverage probability are obtained. Besides, two bootstrap confidence intervals for the parameters of the model are also obtained. Further, by assuming both gamma and non-informative priors for the unknown parameters, Bayes estimates of the parameters, system reliability and hazard rate functions with their bias, SEs, AABias and width of the Bayes credible interval along with coverage probability ( C p ) are obtained. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. Finally, we analyze one real data set to illustrate the results derived.
ISSN:0975-6809
0976-4348
DOI:10.1007/s13198-019-00835-4