Extensions of system signatures to dependent lifetimes: Explicit expressions and interpretations

TL;DR

This paper extends the concept of system signatures to dependent component lifetimes, providing explicit formulas, computational methods, and interpretations, thereby broadening the applicability of system reliability analysis beyond independent components.

Contribution

It introduces an explicit expression for system signatures with dependent lifetimes, including formulas for independent cases and a least squares interpretation.

Findings

Explicit formula for dependent lifetimes

Simplified computation for independent lifetimes

Interpretation via least squares approximation

Abstract

The concept of system signature was introduced by Samaniego for systems whose components have i.i.d. lifetimes. We consider its extension to the continuous dependent case and give an explicit expression for this extension as a difference of weighted means of the structure function values. We then derive a formula for the computation of the coefficients of these weighted means in the special case of independent continuous lifetimes. Finally, we interpret this extended concept of signature through a natural least squares approximation problem.