Most practically collected datasets are plagued with issues of incompleteness and inaccuracies which will cause erroneous reliability modeling and poor maintenance decisions. This work outlines an investigation into the use of Heuristic techniques to estimate the parameters of a stochastic life distribution by using failure data with Truncation and Censoring. A Maximum Likelihood Estimation (MLE) approach was utilized in which the Log-Likelihood function is modified to account for the Truncation and Censoring factors. A Differential Evolution (DE) algorithm developed in MATLAB R2013a minimizes the Negative Log Likelihood (NLL) function and obtains optimum parameters for the 2 Parameters (2-P) Weibull distribution. Results obtained from a series of designed experimental tests generalized the relationship between the increasing levels of Truncation and Censoring individually on the β and η parameters. The impact of the modified NLL technique was examined under cases of Left Truncated and Right Censored (LTRC) data through evaluations of the MSE metric which were compared to estimations made under the normal NLL equation. Truncation and Censoring percentages were increased from 0% to 50% for testing the modified NLL approach. It is clear from the low MSE values (error) that this approach is successful at estimating the parameters closer to the true values. This approach was applied to failure data of a Gas Engine Power Generator utilized in Offshore Gas Production. The results were compared with those obtained from traditional Weibull Analysis in the ReliaSoft Weibull/Alta package.