Reliability Analysis for Two Components Connected in Parallel with Lindley Probability Model
DOI:
https://doi.org/10.6000/1929-6029.2015.04.02.5Keywords:
Reliability R = P(Y<X), Lindley distribution, Maximum Likelihood Estimator, Moment Estimator.Abstract
Reliability of structures has been discussed by several authors using probability models. Some of the early researches have been discussed by Birnbaum (1956) [1] in which two independent variables X and Y are defined as “Strength” and “Stress” respectively.
This research is an extension of Mann- Whitney paper (1947) [2] on P(Y<X). Beg (1979c, 1980b, 1980c) [3-5] estimated reliability i.e R = P(Y<X), by taking two parameter Pareto and Power function distributions. Gupta and Gupta (1990) [6] have found point estimates of R=P(aX> bY) by Maximum likelihood and MVUE of R. In the present paper we have considered R=P(Y<X) where X and Y independently follow Lindley distribution. The MLE and Moment estimators of the distribution and then that of R have been found. A simulation study has been done to estimate biasedness and Confidence interval of R.
References
Birnbaum ZW. On a use of Mann-Whitney statistics. Proc. Third Berkeley Symp. in Math. Statist. Probab., University of California Press 1956; Vol. 1: pp. 13-17. DOI: https://doi.org/10.1525/9780520313880-005
Mann H, Whitney D. On a test whether one of two random variables is stochastically larger than the other. Ann Math Stat 1947; 18: 50-60. DOI: https://doi.org/10.1214/aoms/1177730491
Beg MA. Estimation of Pr(Y DOI: https://doi.org/10.1109/TR.1979.5220665
Beg MA. On the estimation of P(Yhttp://dx.doi.org/10.1007/BF01893574 DOI: https://doi.org/10.1007/BF01893574
Beg MA. Estimation of Pr(Y < X) for truncation parameter distri-bution Communication in Statistics: Theory and methods 1980c; 9(3): 327-345. DOI: https://doi.org/10.1080/03610928008827882
Gupta RD, Gupta RC. Estimation of Pr(a′x > b′y) in the multivariate normal case. Statistics 1990; 21(1): 91-97. DOI: https://doi.org/10.1080/02331889008802229
Al-Mutairi ME, Ghitany, Kundu D. Inferences on Stress-Strength Reliability from Lindley Distribution 2010.
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Copyright (c) 2015 Ehtesham Hussain, Masood ul Haq
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