Determining the optimal design for complex systems using a reliability signature

Abstract

In reliability analysis, the structure-function is a commonly used mathematical representation of the studied system. A signature vector is used for systems with independently and identically distributed (i.i.d.) component lifetimes. Each element in the signature represents the probability that the failure of the corresponding component will fail the entire system. This paper aims to provide a comprehensive understanding of assessing the performance of two complex systems for optimal communication design. The study compares two systems with the same components using signatures, expected cost rate, survival signature, and sensitivity to determine which system is preferred. It also provides several sufficient conditions for comparing the lifetimes of two systems based on the usual stochastic order. The results are applied to two communication systems that have the same components. The mathematical properties presented in the study have been proven to enable efficient weighting of the optimal design.