The Receiver Operating Characteristic (ROC) curve generated based on assuming a constant shape Bi-Weibull distribution is studied. In the context of ROC curve analysis, it is assumed that biomarker values from controls and cases follow some specific distribution and the accuracy is evaluated by using the ROC model developed from that specified distribution. This article assumes that the biomarker values from the two groups follow Weibull distributions with equal shape parameter and different scale parameters. The ROC model, area under the ROC curve (AUC), asymptotic and bootstrap confidence intervals for the AUC are derived. Theoretical results are validated by simulation studies.