A median–based group acceptance sampling plan under the Poisson–Lomax distribution for truncated life tests

In this study, we present a median-based group acceptance sampling plan (GASP) under a truncated life test, assuming that the lifetime of an item follows a flexible three-parameter Poisson-Lomax distribution (PLD). The median lifetime is used as a robust quality index to determine the design parameters of the sampling plan, including the acceptance number, number of groups, and test termination time, while satisfying the specified producer and consumer risks. The performance of the proposed plan is evaluated using operational characteristic (OC) curves and extensive numerical results. The findings indicate that the proposed GASP efficiently reduces the required sample size, inspection time, and cost, particularly for skewed and heavy-tailed datasets. Furthermore, the unknown parameters of the PLD distribution were estimated using the maximum likelihood estimation (MLE) method based on multiple real-life datasets to demonstrate the model applicability. A comparative analysis with existing GASP based on competing lifetime distributions demonstrates that the proposed GASP achieves superior efficiency, requiring fewer testing units while maintaining the specified risk levels.