Since at least a decade, Machine Learning has attracted the interest of researchers. Among the topics of discussion is the application of Machine Learning (ML) and Deep Learning (DL) to the healthcare industry. Several implementations are performed on the medical dataset to verify its precision. The four main players, True Positive (TP), True Negative (TN), False Positive (FP), and False Negative (FN), play a crucial role in determining the classifier's performance. Various metrics are provided based on the main players. Selecting the appropriate performance metric is a crucial step. In addition to TP and TN, FN should be given greater weight when a healthcare dataset is evaluated for disease diagnosis or detection. Thus, a suitable performance metric must be considered. In this paper, a novel machine learning metric referred to as Healthcare-Critical-Diagnostic-Accuracy (HCDA) is proposed and compared to the well-known metrics accuracy and ROC_AUC score. The machine learning classifiers Support Vector Machine (SVM), Logistic Regression (LR), Random Forest (RF), and Naive Bayes (NB) are implemented on four distinct datasets. The obtained results indicate that the proposed HCDA metric is more sensitive to FN counts. The results show, that even if there is rise in %FN for dataset 1 to 10.31 % then too accuracy is 83% ad HCDA shows correlated drop to 72.70 %. Similarly, in dataset 2 if %FN rises to 14.80 for LR classifier, accuracy is 78.2 % and HCDA is 63.45 %. Similar kind of results are obtained for dataset 3 and 4 too. More FN counts result in a lower HCDA score, and vice versa. In common exiting metrics such as Accuracy and ROC_AUC score, even as the FN count increases, the score increases, which is misleading. As a result, it can be concluded that the proposed HCDA is a more robust and accurate metric for Critical Healthcare Analysis, as FN conditions for disease diagnosis and detection are taken into account more than TP and TN.