On Reliability Function of a <i>k</i>-out-of-<i>n</i> System with Decreasing Residual Lifetime of Surviving Components after Their Failures

Abstract

We consider the reliability function of a k-out-of-n system under conditions that failures of its components lead to an increase in the load on the remaining ones and, consequently, to a change in their residual lifetimes. Development of models able to take into account that failures of a system’s components lead to a decrease in the residual lifetime of the surviving ones is of crucial significance in the system reliability enhancement tasks. This paper proposes a novel approach based on the application of order statistics of the system’s components lifetime to model this situation. An algorithm for calculation of the system reliability function and two moments of its uptime has been developed. Numerical study includes sensitivity analysis for special cases of the considered model based on two real-world systems. The results obtained show the sensitivity of system’s reliability characteristics to the shape of lifetime distribution, as well as to the value of its coefficient of variation at a fixed mean.

Keywords

• <i>k</i>-out-of-<i>n</i> system
• dependent failures
• order statistics
• reliability characteristics
• sensitivity analysis