In this study, a group acceptance sampling plan was proposed when the lifetime of an item follows the Darna distribution (DD). The mean served as a quality parameter to determine the design parameters, including the acceptance number and minimum group size, under a specified test termination time and consumer risk. The operating characteristic values were presented graphically and in tabular form. The minimum group size and operating characteristic values were obtained for various values of the distribution parameters, and the results were illustrated with an example. To illustrate the applicability of the proposed plan, two real-life data sets of failure times in minutes and weeks were analyzed as practical examples. It is preferable to choose higher $t/{\mu }_0$ ( ${\mu }_0$ is a given mean value) values to minimize the required number of groups and, hence, reduce the overall cost and inspection effort. In addition, choosing suitable values of $r$ ( $r$ is the size of the group) and $t/{\mu }_0$ ensures a balance between the inspection effort and the risk of the producer.

The integration of Internet of Medical Things (IoMT) devices into are systems has raised significant cybersecurity concerns, especially regarding threats to patient safety and the protection of sensitive medical data. This research proposes a novel hybrid machine learning framework aimed at improving the detection and mitigation of cyberattacks in IoMT environments. Our approach combines random forest, AdaBoost, and bagging algorithms to identify various attack vectors across different IoMT networks. We evaluate our framework using a comprehensive IoMT traffic dataset that includes different communication protocols. Using advanced statistical profiling and ensemble classification models, our system achieves high detection performance while significantly reducing false positive rates compared to traditional methods. The hybrid model demonstrates an exceptional precision of 99.92%, ensuring reliable differentiation between benign and malicious network traffic and minimizing disruptions in critical healthcare environments. Experimental validation across various attack scenarios confirms the effectiveness of the framework in addressing the unique security challenges posed by resource-constrained IoMT devices and heterogeneous communication protocols.