On the Comparison of Classical and Bayesian Methods of Estimation of Reliability in Multicomponent Stress-Strength Model for a Proportional Hazard Rate Model

Taruna Kumari¹ and Anupam Pathak^2,

¹Department of Statistics, University of Delhi, Delhi-110007, India

²Department of Statistics, Ramjas College, University of Delhi, Delhi-110007, India

Cite this paper:
Taruna Kumari and Anupam Pathak. On the Comparison of Classical and Bayesian Methods of Estimation of Reliability in Multicomponent Stress-Strength Model for a Proportional Hazard Rate Model. American Journal of Applied Mathematics and Statistics. 2019; 7(4):152-160. doi: 10.12691/ajams-7-4-5

Abstract

In this article, we consider a multicomponent stress-strength model which has k independent and identical strength components X₁, X₂, …, X_k and each component is exposed to a common random stress Y. Both stress and strength are assumed to have proportional hazard rate model with different unknown power parameters. The system is regarded as operating only if at least s out of k(1≤s≤k) strength variables exceeds the random stress. Reliability of the system is estimated by using maximum likelihood, uniformly minimum variance unbiased and Bayesian methods of estimation. The asymptotic confidence interval is constructed for the reliability function. The performances of these estimators are studied on the basis of their mean squared error through Monte Carlo simulation technique.

Keywords:
proportional hazard rate model; maximum likelihood estimation uniformly minimum variance unbiased estimation Bayesian estimation; asymptotic confidence interval multicomponent reliability.

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