improved fuzzy bayesian reliability analysis of coherent systems via the‎‎ α‎-pessimistic method

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.