Stochastic Orderings of the Idle Time of Inactive Standby Systems

Abstract

In this paper, we consider a failed cold standby system and obtain stochastic bounds on the idle time of such systems. We state and prove that if the last spare in the system is exponentially distributed and if the components have log-concave lifetime distributions, then the idle time of a failed cold standby system is smaller than the sum of the idle times of the components in the system according to the likelihood ratio order. In order to compare the idle time of two cold standby systems with different numbers of spares and different observation times of the failure in terms of the likelihood ratio order, an additional result is presented. Finally, we establish sufficient conditions for the usual stochastic ordering between the idle time of a cold standby system of size two and the sum of the idle times of the components in the system. We provide several examples to show that the results are achievable.

A Stochastic Analysis of Computing Models in Computer System Reliability Based on Hardware and Software

“…Semantic set firing probabilities are significant exclusively to collective agents. In a similar way, trustworthiness R (2) and R (3) of pathwaysQ2 and Q3can be found. Next, the system's dependability is provided by R(T) = R1C1R2C2R3C3(q1R (1) + q2R (2) )…”

“…In a similar way, trustworthiness R (2) and R (3) of pathwaysQ2 and Q3can be found. Next, the system's dependability is provided by R(T) = R1C1R2C2R3C3(q1R (1) + q2R (2) )…”

“…One may compute the dependability the bridge network is identifiable in the the data flow graph as R(Bridge Network) = R (3) + R (1) [(1-RD)+RD(1-RC)]+R (2) (1-RA)RD(1-RD)+R (4) Where path Qj dependability is denoted by R (1) . Units A, B, C, D, and F have reliabilities denoted as RB, RA, RD, RC, and RF, in that order.…”