# zbMATH — the first resource for mathematics

Estimation of the reliability of a stress-strength system from power Lindley distributions. (English) Zbl 1325.62048
Summary: We are interested in the estimation of the reliability parameter $$R = P(X > Y)$$ where $$X$$, a component strength, and $$Y$$, a component stress, are independent power Lindley random variables. The point and interval estimation of $$R$$, based on maximum likelihood, nonparametric and parametric bootstrap methods, are developed. The performance of the point estimate and confidence interval of $$R$$ under the considered estimation methods is studied through extensive simulation. A numerical example, based on a real data, is presented to illustrate the proposed procedure.

##### MSC:
 62F10 Point estimation 62F12 Asymptotic properties of parametric estimators 62F40 Bootstrap, jackknife and other resampling methods 62F15 Bayesian inference 62N05 Reliability and life testing
Full Text:
##### References:
 [1] DOI: 10.1080/03610926.2011.563011 · Zbl 1294.62036 [2] Bader M.G., Progress in Science and Engineering Composites 4 pp 1129– (1982) [3] DOI: 10.1080/00401706.1970.10488633 [4] Downton F., Technometrics 15 pp 551– (1973) [5] Efron B., An Introduction to Bootstrap (1998) [6] DOI: 10.1016/j.matcom.2007.06.007 · Zbl 1140.62012 [7] DOI: 10.1081/STA-100107696 · Zbl 1009.62513 [8] DOI: 10.1016/j.csda.2005.05.005 · Zbl 1445.62268 [9] DOI: 10.1016/j.csda.2008.10.014 · Zbl 1452.62726 [10] DOI: 10.1023/A:1003910408020 · Zbl 0938.62014 [11] DOI: 10.1080/02331889008802229 · Zbl 0699.62053 [12] DOI: 10.1142/9789812564511 [13] DOI: 10.1007/s00184-006-0074-7 · Zbl 1433.62061 [14] DOI: 10.1007/s001840400345 · Zbl 1079.62032 [15] DOI: 10.1109/TR.2006.874918 [16] DOI: 10.1016/j.spl.2009.05.026 · Zbl 1169.62012 [17] Lehmann L. E., Theory of Point Estimation. 2nd ed. (1998) · Zbl 0916.62017 [18] Lindley D.V., Journal of the Royal Statistical Society B 20 pp 102– (1958) [19] DOI: 10.1002/nav.3800170203 · Zbl 0205.23001 [20] DOI: 10.1081/SAC-200055741 · Zbl 1065.62172 [21] DOI: 10.1080/03610920802162664 · Zbl 1292.62041 [22] Reiser B., Technometrics 28 pp 253– (1986)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.