Algorithms and formulas for conversion between system signatures and reliability functions

TL;DR

This paper develops formulas and algorithms for converting between system signatures and reliability functions in semicoherent systems with i.i.d. component lifetimes, facilitating system analysis and comparison.

Contribution

It introduces new conversion formulas and efficient algorithms for deriving signatures from reliability functions and vice versa, enhancing analysis tools for system reliability.

Findings

Derived explicit conversion formulas between signatures and reliability functions.

Developed algorithms for efficient computation of signatures from reliability data.

Showed how to compute signatures from reliability functions using differentiation and integration.

Abstract

The concept of signature is a useful tool in the analysis of semicoherent systems with continuous and i.i.d. component lifetimes, especially for the comparison of different system designs and the computation of the system reliability. For such systems, we provide conversion formulas between the signature and the reliability function through the corresponding vector of dominations and we derive efficient algorithms for the computation of any of these concepts from the other. We also show how the signature can be easily computed from the reliability function via basic manipulations such as differentiation, coefficient extraction, and integration.