Survival Signature Approach for Reliability Evaluation of Linear Consecutive \(k\)-out-of-\(n\):\(G\) System - Deepak,; Chopra, Garima (Communications in Mathematics and Applications, 2024)
The present study concentrates on computing the reliability function for linear consecutive \(k\)-out-of-\(n:G\) system with independent and identically distributed components. For systems where \(2k \ge n\), we establish a formulation for the system survival signature. This is subsequently utilized to find a non-recursive representation of system reliability. The attained closed-form representation of system reliability empowers us to easily evaluate the performance of higher-order consecutive systems. The system signature is also evaluated with the assistance of the survival signature. Additionally, a method for calculating the system hazard rate function in light of its components’ hazard rate functions is suggested. Both exponential and Pareto distributions are considered in assessing the reliability function for such systems. A numerical example related to a quality control system provides a concrete illustration of the results achieved through the proposed method.
Keywords: Reliability; System signature; Survival signature; Linear consecutive k-out-of-n : G system; Hazard rate function