Document Type : Original Article

Authors

• Mahnaz Mirzayi ¹
• Reza Zarei ²
• Gholamhossein Yari ³
• Mohammad Hassan Behzadi ¹

¹ Department of Statistics, SR.C., Islamic Azad University, Tehran, Iran

² Department of Statistics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.

³ Department of Statistics‎, School of Mathematics‎, ‎Iran University Science and Technology‎, ‎Tehran‎, ‎Iran

Abstract

In real-world reliability analysis, the underlying data and prior knowledge are often imprecise, posing significant challenges to classical probabilistic models. This study presents a novel fuzzy Bayesian approach for analyzing the reliability of coherent systems under imprecise prior information, where system lifetimes follow a Pascal distribution. We construct uncertain Bayes estimators using both squared error and precautionary loss functions by modelling the system reliability as a fuzzy random variable with a prior fuzzy distribution. A key innovation of the proposed approach is the application of the ‎α-pessimistic method, which allows for the estimation process to be carried out without relying on complex non-linear programming, a common limitation in existing literature. Instead, this technique simplifies the computational procedure while enhancing interpretability and analytical tractability. The framework is applied to coherent systems, including parallel, series, and k-out-of-m structures, using Mellin transform techniques to derive the estimators. A numerical example is provided to demonstrate the practical applicability and effectiveness of the proposed method.

Keywords

• Fuzzy Bayesian Estimation‎
• System Reliability
• α‎-Pessimistic Technique
• Imprecise Prior Information
• Coherent Systems