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

摘要

Let X _1, X _2, and X _3 be independent random variables with absolutely continuous distributions having the common support [0, ~∞). We show that if X _1≤ _(hr[mrl,lr])X _3 and X _2≤ _(hr[mrl,lr])X _3, then max≤X _1, X _2≤≤ _(hr[mrl,lr])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).