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Likelihood ratio order of parallel systems under multiple-outlier models. (English) Zbl 1394.90238
Summary: This paper studies the likelihood ratio ordering of parallel systems under multiple-outlier models. We introduce a partial order, the so-called \(\theta\)-order, and show that the \(\theta\)-order between the parameter vectors of the parallel systems implies the likelihood ratio order between the systems.
MSC:
90B25 Reliability, availability, maintenance, inspection in operations research
60E15 Inequalities; stochastic orderings
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[1] Balakrishnan, N., and P. Zhao. 2013. Ordering properties of order statistics from heterogeneous populations: a review with an emphasis of some recent developments. Probability in the Engineering and Informational Sciences 27:403-43. · Zbl 1288.60023
[2] Da, G., W. Ding, and X. Li. 2010. On hazard rate ordering of parallel systems with two independent components. Journal of Statistical Planning and Inference 140:2148-54. · Zbl 1188.90076
[3] Dykstra, R., S. C. Kochar, and J. Rojo. 1997. Stochastic comparisons of parallel systems of heterogeneous exponential components. Journal of Statistical Planning and Inference 65:203-11. · Zbl 0915.62044
[4] Mao, T., and T. Hu. 2010. Equivalent characterizations on orderings of order statistics and sample ranges. Probability in the Engineering and Informational Sciences 24:245-62. · Zbl 1193.60025
[5] Misra, N., and A. K. Misra. 2013. On comparison of reversed hazard rates of two parallel systems comprising of independent gamma components. Statistics & Probability Letters 83:1567-70. · Zbl 1287.60029
[6] Pledger, P., and F. Proschan. 1971. Comparison of order statistics and of spacings from heterogeneous distributions. In Optimizing methods in statistics, ed. J. S. Rustagi, 89-113. New York: Academic Press. · Zbl 0263.62062
[7] Shaked, M., and J. G. Shanthikumar. 2007. Stochastic orders. New York: Springer. · Zbl 0806.62009
[8] Shaked, M. 2013. Comments on the survey by Balakrishnan and Zhao. Probability in the Engineering and Informational Sciences 27:445-9. · Zbl 1295.60025
[9] Torrado, N., and S. C. Kochar. 2015. Stochastic order relations among parallel systems from Weibull distributions. Journal of Applied Probability 52:102-16. · Zbl 06441354
[10] Yan, R., G. Da, and P. Zhao. 2013. Further results for parallel systems with two heterogeneous exponential components. Statistics 47:1128-40. · Zbl 1440.62363
[11] Zhao, P., and N. Balakrishnan. 2012. Stochastic comparisons of largest order statistics from multiple outlier exponential models. Probability in the Engineering and Informational Sciences 26:159-82. · Zbl 1275.62046
[12] Zhao, P., Y. Hu, and Y. Zhang. 2015. Some new results on largest order statistics from multiple-outlier gamma models. Probability in the Engineering and Informational Sciences 29:597-621. · Zbl 1373.62215
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