Signature reliability of linear consecutive k-out-of-n:G system using universal generating function approach

This paper investigates the signature reliability of a linear consecutive -out-of-: system using the universal generating function (UGF) technique. The system comprises n components, where only k consecutive ones need to function for the entire system to operate. As a starting point, a linear consecutive -out-of-: G system is modeled to derive its reliability function, which is then converted into polynomial form. The study next analyzes the system’s tail-signature to support the evaluation of its signature reliability. facilitate the evaluation of its signature reliability. The Barlow-Proschan index is applied to assess the system's overall reliability. Finally, the study derives key performance metrics including the minimal signature, expected lifespan, and actual cost rate for the proposed configuration.