A four-parameter continuous probability model called the Weibull log-logistic {Exponential} distribution (WLLED) was introduced and studied in this research using T-log-logistic {Exponential} distribution via T-R{Y} framework to extend the two-parameter log-logistic distribution. The objective of this research is to explore the versatility and flexibility of the log-logistic and Weibull distributions in modeling lifetime data. Some basic structural properties which include the reliability measures and hazard function, cumulative hazard function, Moment, Quantile, skewness, kurtosis, mixture representation, order statistics and asymptotic behavior of the WLLED were obtained and established. The shape of the new four parameter distribution is also investigated. A simulation study was conducted to evaluate the MLE estimates, bias, and standard error for various parameter combinations and different sample sizes. The efficiency of the WLLE distribution was compared with other related distribution from the literature using five goodness-of-fit statistics: AIC, CAIC and BIC, Anderson-Darling A* and Cramér-Von Mises W*, methods of comparison. The method of maximum likelihood estimation was proposed in estimating its parameters. An application to the survival times of 121 patients with breast cancer dataset was provided and the WLLED displays a good fit. Finally, it is recommended that the WLLED can be used for modeling positively skewed real-life data.