Signature-based reliability study of r-within-consecutive-k-out-of-n: F systems

Abstract

In the present chapter, we carry out a reliability study of the r-within-consecutive-k-out-of-n: F systems with independent and identically distributed components. A simulation algorithm is proposed for determining the coordinates of the signature vector of the r-within-consecutive-k-out-of-n: F structures, while several stochastic orderings among the lifetimes of several consecutive-type structures are also established. In addition, explicit signature-based expressions for the reliability function, mean residual lifetime, and conditional mean residual lifetime of the aforementioned models are provided, while several numerical results are also presented. For illustration purposes, well-known multivariate distributions for modeling the lifetimes of the components of the r-within-consecutive-k-out-of-n: F structure are considered in some details. © 2021 Elsevier Inc. All rights reserved.