Reliability Analysis for Two Components Connected in Parallel with Lindley Probability Model

Authors

  • Ehtesham Hussain Department of Statistics, University of Karachi, Karachi, Pakistan
  • Masood ul Haq Usman Institute of Technology, Karachi, Pakistan

DOI:

https://doi.org/10.6000/1929-6029.2015.04.02.5

Keywords:

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.

Author Biography

Ehtesham Hussain, Department of Statistics, University of Karachi, Karachi, Pakistan

Statistics

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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Published

2015-05-21

How to Cite

Hussain, E., & Haq, M. ul. (2015). Reliability Analysis for Two Components Connected in Parallel with Lindley Probability Model. International Journal of Statistics in Medical Research, 4(2), 199–202. https://doi.org/10.6000/1929-6029.2015.04.02.5

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Section

General Articles

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