Abstract
The problem of estimation reliability in a multicomponent stress-strength model, when the system consists of k components have strength each compo- nent experiencing a random stress, is considered in this paper. The reliability of such a system is obtained when strength and stress variables are given by Lindley distribution. The system is regarded as alive only if at least r out of k (r < k) strength exceeds the stress. The multicomponent reliability of the system is given by Rr,k . The maximum likelihood estimator (M LE), uniformly minimum variance unbiased estimator (UMVUE) and Bayes esti- mator of Rr,k are obtained. A simulation study is performed to compare the different estimators of Rr,k . Real data is used as a practical application of the proposed model.
Highlights
The Lindley distribution originally developed by Lindley (1958, 1965) in the context of Bayesian statistics, is a counter example of fiducial statistics
We have considered the problem of estimation reliability in a multicomponent stress-strength model Rr,k = P [Yr:n1 < Xk:n2 ] for which the stress and strength variables are given by a Lindley distribution
By simulation we made a comparison between the maximum likelihood and Bayes estimators
Summary
The Lindley distribution originally developed by Lindley (1958, 1965) in the context of Bayesian statistics, is a counter example of fiducial statistics. Ghitany & Atieh (2008) studied the mathematical and statistical properties of the Lindley distribution. They have shown that this distribution is better a model than the well-known exponential distribution in some particular cases. Many authors have discussed the Lindley distribution as a model of lifetime data such as Krishna & Kumar (2011), Singh, Singh & Singh (2008) and Singh, Gupta & Sharma (2014), and Al-Mutairi et al (2013) studied stress-strength model. The inverse Lindley distribution discussed as stress-strength model has been studied by Sharma, Singh, Singh & Agiwal (2014, 2015).
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