关于一类新的并联系统剩余寿命的研究

Study of the Residual Life of a New Class of Parallel System

研究由n个独立不同分布的元件组成的并联系统在3种条件下的平均剩余寿命.第一种,在t(t>0)时刻至多有(r-1)个元件失效的条件下,并联系统的平均剩余寿命,并以指数分布为例加以说明;第二种,在t时刻至少有r个元件失效,至多有m-1(m<n)个元件失效的条件下,并联系统的平均剩余寿命,并以指数分布为例加以说明;第三种,在t1时刻至少有r个元件失效,至多有(m-1)个元件失效,且在t2(t2>t1)时刻恰好有k个元件失效的情况下并联系统的平均剩余寿命.最后,考虑了元件寿命服从指数分布时的特殊情形.

The mean residual life function of parallel systems with n independent but not identically distributed components is investigated in three cases. Firstly, under the condition that,at time t （t ~〉0） and the total number of failures of the components is no more than （r-1） ,the mean residual life function of the parallel system is studied and an example of exponential distribution is taken to illustrate it. Secondly, under the condition that,at time t and the total number of failures of the components is at least r and no more than m-1（m〈n）, the mean residual life function of the parallel system is studied and an example of exponential distribution is taken to illustrate it. Thirdly, under the condition that, at time t1 ,the total number of failures of the components is at least r and no more than m- 1（m〈n）, and at time t2 （t2〉t1 ） and the total number of failures is k, the mean residual life function of the parallel system is studied. Finally, in the case of exponential distribution,its especial expression form is written out.