Model construction in Stochastic Binary Systems.

Abstract

A Stochastic Binary System (SBS) is a mathematical model representing a multicomponent on-off system, where components are subject to random failures. Formally, an SBS is defined as a triad (S, p, ϕ), where S = {1, . . . ,m} is a ground set of components, p = (p1, . . . , pm) ∈ [0, 1]m represents their elementary reliabilities, and ϕ : {0, 1}m → {0, 1} is the logical rule or structure function that determines the system’s state based on the states of its components. While previous studies have typically assumed perfect information about the system, this work focuses on a data-driven approach to model construction. Specifically, we develop and evaluate machine learning (ML) and deep learning (DL) models to approximate the structure function ϕ of an SBS using only a random subset of its possible states. The primary objectives are to maximize accuracy on a test set and investigate trade-offs between accuracy, computational efficiency, and model complexity. Furthermore, we analyze the generalizability of the models by evaluating their performance on all possible unobserved states of the system. Experimental results are promising, with some models achieving perfect accuracy across all possible states in systems of moderate size, demonstrating the effectiveness of this approach for approximating stochastic systems.