k-out-of-N系统的随机比较

Stochastic Comparisons of k-out-of-N System

设 {Xn,n≥ 1}是独立非负随机变量序列 ,N是正整值的随机变量且与 {Xn,n≥ 1}独立 .考虑由寿命为X1,… ,XN 的N个部件组成的k -out -of-N系统 (系统正常当且仅当N个部件中至少k个正常 )的寿命 。

Let {X n,n≥1} be a sequence of independent non negative random variables and let N be a positive interger valued random variable which is independent of the {X n,n≥1}.We obtain some stochastic comparison results involving lifetimes of k -out-of- N system(a system of N components which functions if at least k components function)whose components have lifetimes X 1,...,X N on hazard ordering.