General Multi-State Rework Network and Reliability Algorithm

TL;DR

This paper critiques an existing algorithm for rework network reliability, introduces a more accurate general model with fewer limitations, and proposes a new algorithm to compute reliability in multi-state rework networks.

Contribution

It corrects the inaccuracies in Song's algorithm, develops a novel state distribution model, and presents a new reliability calculation algorithm for multi-state rework networks.

Findings

Song's algorithm is proven incorrect.

A new, more accurate model with fewer limitations is proposed.

An algorithm for reliability calculation using the new model is introduced.

Abstract

A rework network is a common manufacturing system, in which flows (products) are processed in a sequence of workstations (nodes), which often results in defective products. To improve the productivity and utility of the system, the rework network allows some of the defective products to go back to the "as normal" condition after the rework process. In a recent study, Song proposed an algorithm to correct more than 21 archive publications regarding the rework network reliability problem, which is an important real-life problem. However, we prove that Song's proposed algorithm is still incorrect. Additionally, we provide an accurate general model based on the novel state distribution with a smaller number of limitations. Furthermore, we propose an algorithm to calculate the reliability of the multi-state rework networks using the proposed novel state distributions.