# zbMATH — the first resource for mathematics

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
Full Text:
##### References:
 [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
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.