Reliability assessment through group acceptance sampling under the Darna distribution

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.