Reliability analysis of semicoherent systems through their lattice polynomial descriptions

TL;DR

This paper explores the relationship between structure functions and lattice polynomial functions in semicoherent systems, providing exact formulas for reliability analysis and highlighting their equivalence to distribution functions of lattice polynomials.

Contribution

It introduces a unified approach connecting structure functions and lattice polynomial representations for precise reliability calculations in semicoherent systems.

Findings

Derived exact formulas for system reliability using lattice polynomial functions

Established the equivalence between reliability computation and distribution functions of lattice polynomials

Highlighted the parallelism between structure functions and lattice polynomial descriptions

Abstract

A semicoherent system can be described by its structure function or, equivalently, by a lattice polynomial function expressing the system lifetime in terms of the component lifetimes. In this paper we point out the parallelism between the two descriptions and use the natural connection of lattice polynomial functions and relevant random events to collect exact formulas for the system reliability. We also discuss the equivalence between calculating the reliability of semicoherent systems and calculating the distribution function of a lattice polynomial function of random variables.