A lifetime distribution model was proposed by Dimitrakopoulou, et al. in 2007 . This model has three parameters and includes the Weibull distribution as a special case. Therefore, this is a Weibull related distribution model and it has decreasing, increasing, bathtub and upside-down bathtub-shaped failure rate. Since this distribution model has more flexibility than the conventional 2- and 3-parameter Weibull distributions in modeling the lifetime data, it is of interest to have a study on its statistical characteristics and explore the real application of the model to modeling time to failure data. The objective of this paper is to investigate the parameter estimation of this 3-parameter Weibull related model by graphical approach with short discussion on its statistical characteristics. The procedure in detail for parameter estimation of the model is presented and its usefulness is demonstrated by two real examples.