R-scripts for approximating complex coherent systems by mixed systems with IID components

Abstract

This document provides a comprehensive user guide and technical documentation for a collection of R scripts: BD.R, QP.R, MiniMax.R, and CVaR.R. These computational tools have been developed to facilitate the reliability analysis of complex coherent systems—particularly those with general dependence structures and component redundancy—by approximating their reliability functions using mixed systems with independent and identically distributed (IID) components. The guide outlines the theoretical foundations, required packages, and step-by-step usage instructions for four distinct approximation methodologies: Bernstein polynomial sequences, quadratic programming for L2 norm minimization, and linear programming for both L∞ norm and Conditional Value-at-Risk (CVaR) minimization. To ensure a clear understanding and facilitate practical implementation, the documentation includes specific use-case examples for each script, directly replicating the results analyzed in the main research article Arriaza et al. (2026). Finally, this resource provides researchers the necessary tools to apply these approximation techniques in their own reliability studies.