Bayesian reliability estimation of weighted exponential-lindley distribution with intuitionistic fuzzy lifetime data

This paper explores the Bayesian reliability estimation of the Weighted Exponential-Lindley distribution (WXLD) using intuitionistic fuzzy lifetime data. The study begins by extending the definitions of probability, conditional probability, and likelihood functions to accommodate intuitionistic fuzzy observations. The focus lies on Bayesian estimation approaches for the one-parameter WXLD, along with reliability analysis based on intuitionistic fuzzy lifetime data. For this, a gamma prior is adopted, and parameter and reliability estimations are carried out under the square error loss function (SELF). Given the complexity of integrals, the Lindley approximation and Tierney and Kadane (T-K) approximation is employed to approximate Bayesian estimates. For illustrative purposes, the proposed estimation methods are applied to a simulated dataset, showcasing their practical relevance and applicability. Finally, the proposed methods are validated using real-world data, affirming their effectiveness in practical applications.