New results on stochastic comparisons of two-component series and parallel systems

作者：Misra Neeraj; Misra Amit Kumar^*

来源：Statistics & Probability Letters, 2012, 82(2): 283-290.

DOI：10.1016/j.spl.2011.10.010

• Hazard rate order
• Likelihood ratio order
• Mean residual life order
• Reversed hazard rate order
• Usual stochastic order

Let X-1, X-2, and X-3 be independent random variables with absolutely continuous distributions having the common support [0, infinity). We show that if X-1 <=(hrfmrl).(lr) X-3 and X-2 <=(hr[mrl.lr) X-3, then max {X-1, X-2} <=(hr[mrl.ir]) max{X-1, X-3}. We also show that if X-2 <=(rh[lr]) X-1 and X-2 <=(rh[lr]) X-3, then min{X-1, X-2} <=(rh[lr]) min{X-1, X-3}. These results generalize and extend some of the results given in Shaked and Shanthikumar (2007, Example 1.C.36, p. 56), Joo and Mi (2010), and Da et al. (2010).

• 出版日期2012-2