Reliability maximization of a load‐sharing system without redundant components

Abstract

This paper considers a problem of determining the optimal number of components for maximizing reliability of a load‐sharing series system in which no redundant components exist. Previously, this problem has been studied numerically, under the assumption that the load–life relationship is described by a power function, and the component follows an exponential or a Weibull lifetime distribution. In this paper, our objective is to obtain analytical results for the optimal number of components given that a general link function explains a load–life relationship and the component follows a general lifetime distribution. We show that the optimal number of components non‐decreases with the elasticity of the link function and the ratio of the component failures sensitive to the changing design load. We also show that the premature failures occurring early in the life of a component affect the optimal solution, depending on whether a link function is used for scaling the nominal failure rate independently of the mission time, or it is used for scaling the nominal life dependently with the mission time. We believe that the result is useful in selecting the number of the components to use in a system when studying design trade‐offs at an early design stage.