Reliability of systems with dependent components based on lattice polynomial description

TL;DR

This paper develops a framework for analyzing the reliability of systems with dependent components using lattice polynomial functions, addressing cases with external dependencies and bounds on component lifetimes.

Contribution

It introduces a general framework for system reliability with dependent components based on lattice polynomial descriptions, including cases with external factors and bounds.

Findings

Formulas for reliability with Bayes-dependent lifetimes

Results for systems with lifetime bounds

Detailed analysis of special cases

Abstract

Reliability of a system is considered where the components' random lifetimes may be dependent. The structure of the system is described by an associated "lattice polynomial" function. Based on that descriptor, general framework formulas are developed and used to obtain direct results for the cases where a) the lifetimes are "Bayes-dependent", that is, their interdependence is due to external factors (in particular, where the factor is the "preliminary phase" duration) and b) where the lifetimes' dependence is implied by upper or lower bounds on lifetimes of components in some subsets of the system. (The bounds may be imposed externally based, say, on the connections environment.) Several special cases are investigated in detail.