Stochastic Comparisons On A New Residual Life And Inactivity Time Of (n-m+1)-out-of-n Systems

Stochastic comparison theory is useful in applied probability、statistics、actuary science、reliability and other fields. This dissertation focus on stochastic comparisons of n independent condition order statistic of identically distributed samples, and stochastic comparisons problem on residual life and inactivity time of(n-m?1)-out-of- n systems is studied.At first, we consider stochastic comparison on the residual life of(n-m?1)-out-of- n systems with n independent identically distributed components under multi monitoring. On the one hand,(n-m?1)-out-of- n system with a set of independent identical components are studied, and according to likelihood ratio order, stochastic comparison on the residual life of a systems with stochastically ordered are conducted. On the other hand, we define(n-m?1)-out-of- n with two sets of independent identical components. if there is a hazard order relation between two sets of independent components of different structure, there is usual stochastic order between residual life of two systems.Next, stochastic comparison on the inactivity time under the double or multi monitoring are developed with two(n-m?1)-out-of- n systems with a set of independent identical components. We are interested in the study of the inactivity time and the mean past time of the system. Some ordering properties basing on the reliability function of the inactivity time are established.