Multicomponent stress-strength reliability estimation based on unit generalized Rayleigh distribution
International Journal of Quality & Reliability Management
ISSN: 0265-671X
Article publication date: 5 March 2021
Issue publication date: 1 November 2021
Abstract
Purpose
The purpose of this article is to derive inference for multicomponent reliability where stress-strength variables follow unit generalized Rayleigh (GR) distributions with common scale parameter.
Design/methodology/approach
The authors derive inference for the unknown parametric function using classical and Bayesian approaches. In sequel, (weighted) least square (LS) and maximum product of spacing methods are used to estimate the reliability. Bootstrapping is also considered for this purpose. Bayesian inference is derived under gamma prior distributions. In consequence credible intervals are constructed. For the known common scale, unbiased estimator is obtained and is compared with the corresponding exact Bayes estimate.
Findings
Different point and interval estimators of the reliability are examined using Monte Carlo simulations for different sample sizes. In summary, the authors observe that Bayes estimators obtained using gamma prior distributions perform well compared to the other studied estimators. The average length (AL) of highest posterior density (HPD) interval remains shorter than other proposed intervals. Further coverage probabilities of all the intervals are reasonably satisfactory. A data analysis is also presented in support of studied estimation methods. It is noted that proposed methods work good for the considered estimation problem.
Originality/value
In the literature various probability distributions which are often analyzed in life test studies are mostly unbounded in nature, that is, their support of positive probabilities lie in infinite interval. This class of distributions includes generalized exponential, Burr family, gamma, lognormal and Weibull models, among others. In many situations the authors need to analyze data which lie in bounded interval like average height of individual, survival time from a disease, income per-capita etc. Thus use of probability models with support on finite intervals becomes inevitable. The authors have investigated stress-strength reliability based on unit GR distribution. Useful comments are obtained based on the numerical study.
Keywords
Acknowledgements
The authors thank the reviewers and Editor for their insightful comments that have led to a substantial improvement to an earlier version of the paper.
Citation
Jha, M.K., Tripathi, Y.M. and Dey, S. (2021), "Multicomponent stress-strength reliability estimation based on unit generalized Rayleigh distribution", International Journal of Quality & Reliability Management, Vol. 38 No. 10, pp. 2048-2079. https://doi.org/10.1108/IJQRM-07-2020-0245
Publisher
:Emerald Publishing Limited
Copyright © 2021, Emerald Publishing Limited