<p>Flexible and parsimonious parametric models for time-to-event data are valuable when hazards depart from simple monotonic shapes. This article aiming at the development of Flexible Exponential-Type Family (FETF), a probability-scale generator that transforms a baseline cumulative distribution function via an exponential-type mapping, and develop the Exponential-Type Weibull (ETW). To validate the theoretical performance of ETW, we derived a closed-form density and hazard expressions, identifiability results, regularity conditions for likelihood inference, and series representations of moments and mean residual life. To evaluate practical performance, we present a comprehensive Monte Carlo benchmarking design that contrasts ETW with Weibull, Inverse-Weibull, Transmuted Inverse-Weibull and Alpha-Power Weibull families across canonical hazard regimes (increasing, decreasing, unimodal) and classical bathtub scenarios (mixture/shifted generators). Simulation metrics include bias, mean squared error, empirical coverage, convergence rates and model-selection (AIC/BIC) frequencies. The empirical caparison of the proposed method on an anonymized Mexican COVID-19 mortality cohort (n = 106), reporting MLEs, information criteria and robust graphical diagnostics (QQ/PP with bootstrap bands, Cox–Snell residuals, total time on test). Numerical finding show ETW is a compact, viable choice when the true hazard is unimodal or otherwise non-monotonic and when an initial zero hazard at time-zero is acceptable, when initial preeminent hazard is existed, transformed or mixture models are superior. We conclude with practical guidance for applied use, explicit limitations of the illustrative dataset, and concrete extension paths.</p>