The purpose of this paper is to estimate the multicomponent reliability by assuming the unit-Gompertz (UG) distribution. Both stress and strength are assumed to have an UG distribution with common scale parameter.
The reliability of a multicomponent stress–strength system is obtained by the maximum likelihood (MLE) and Bayesian method of estimation. Bayes estimates of system reliability are obtained by using Lindley’s approximation and Metropolis–Hastings (M–H) algorithm methods when all the parameters are unknown. The highest posterior density credible interval is obtained by using M–H algorithm method. Besides, uniformly minimum variance unbiased estimator and exact Bayes estimates of system reliability have been obtained when the common scale parameter is known and the results are compared for both small and large samples.
Based on the simulation results, the authors observe that Bayes method provides better estimation results as compared to MLE. Proposed asymptotic and HPD intervals show satisfactory coverage probabilities. However, average length of HPD intervals tends to remain shorter than the corresponding asymptotic interval. Overall the authors have observed that better estimates of the reliability may be achieved when the common scale parameter is known.
Most of the lifetime distributions used in reliability analysis, such as exponential, Lindley, gamma, lognormal, Weibull and Chen, only exhibit constant, monotonically increasing, decreasing and bathtub-shaped hazard rates. However, in many applications in reliability and survival analysis, the most realistic hazard rates are upside-down bathtub and bathtub-shaped, which are found in the unit-Gompertz distribution. Furthermore, when reliability is measured as percentage or ratio, it is important to have models defined on the unit interval in order to have plausible results. Therefore, the authors have studied the multicomponent stress–strength reliability under the unit-Gompertz distribution by comparing the MLEs, Bayes estimators and UMVUEs.
The authors are grateful to reviewers for useful comments that led to significant improvements in the manuscript. The authors also thank the Editor for helpful comments. Yogesh Mani Tripathi gratefully acknowledges the partial financial support for this research work under a grant EMR/2016/001401 Science and Engineering Research Board, India.
Jha, M., Dey, S. and Tripathi, Y. (2019), "Reliability estimation in a multicomponent stress–strength based on unit-Gompertz distribution", International Journal of Quality & Reliability Management, Vol. ahead-of-print No. ahead-of-print. https://doi.org/10.1108/IJQRM-04-2019-0136Download as .RIS
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