<![CDATA[General Background: Fuzzy estimation plays a vital role in enhancing the precision of statistical inference under uncertainty, particularly in reliability theory. Specific Background: Classical estimators often struggle with mixed probability distributions involving both continuous and vague components. Knowledge Gap: Despite the theoretical relevance, limited comparative analysis exists on fuzzy estimators within hybrid exponential-gamma models under varied risk functions. Aim: This study aims to derive and compare various fuzzy estimators for the risk function of a mixed continuous distribution formed by combining the exponential (θ) and Gamma (2,θ) distributions, with mixing proportions β/(β+1) and 1/(β+1), respectively. Results: We derive the corresponding probability density function (pdf), cumulative distribution function (CDF), reliability, and hazard functions. A fuzzy vagueness factor (k̃) is introduced into the hazard equation, and the r-th raw moment [μ′(r)] is formulated. Parameters θ and β are estimated via maximum likelihood, moments, and frequency ratio methods. Novelty: The integration of fuzzy theory into hazard modeling for a quasi-Lindley framework, coupled with comprehensive estimator comparison, offers novel insights. Implications: The findings enhance reliability analysis under fuzzy environments, enabling more robust decision-making in engineering and survival analysis contexts. Highlights: Introduces fuzzy estimation in hazard function modeling. Compares three estimation methods for mixed distributions. Derives complete reliability metrics from a hybrid model. Keywords: Maximum Likelihood, Moment Estimation, Fuzzy Estimator, Hazard Rate, Quasi-Lindley Distribution]]>
