Generalization of reliability in the odd Lindley-G family

This study presents a generalized numerical framework for evaluating the reliability criterion in the odd Lindley-G family of distributions. Although the odd Lindley-G family provides a flexible mechanism for extending classical baseline models, the existing analytical formulation for reliability estimation suffers from two critical limitations: it is restricted to cases where the strength and stress variables share an identical baseline distribution, and its series expansion diverges even under homogeneous baseline conditions. To address these limitations, we develop a robust numerical integration framework that accurately computes reliability for arbitrary and distinct baseline distributions within the odd Lindley-G family. The proposed method is validated through an extensive simulation study and a practical engineering application involving strength and stress data with different baseline distributions. Our findings confirm that the numerical framework not only generalizes the applicability of the odd Lindley-G family but also delivers a stable, accurate, and computationally efficient tool for advanced reliability analysis.

کلیدواژه ها:

Numerical integration ، Odd Lindley-G family ، Stress-strength reliability