Optimizing Group Size using Percentile Based Group Acceptance Sampling Plans with Application

Abstract

The present paper focuses on optimizing the sample size and the acceptance number which are commonly known as design parameters for the group acceptance sampling plan (GASP). Design parameters are analyzed under the assumption that the characteristic of interest for the product follows Another Generalized Transmuted-Exponential (AGTransmuted-Exponential) distribution. Using different values of the quality levels (median lifetime), the values of the Operating Characteristic function is determined. The proposed plan satisfies two types of risks based on producer's point of view and consumer’s point of view at varied stipulated quality levels. Optimization of the sample size, group size and acceptance numbers is obtained through Monte Carlo simulation, for which relevant R codes were developed. Specific R codes are appended for future usage by academia and practitioners from various fields of life. The simulated results of the study are exhibited in the form of tables and explained with relevant examples. Results of the proposed GASP are compared with plan parameters obtained using MLE estimates of AGTransmuted-Exponential distribution and also by design parameters obtained using mean as quality level. Results of the study exhibited that Median as a quality parameter resulted in the decrease of group size and acceptance number simultaneously at all quality levels. Easy to follow the methodology of the current paper will open new vistas for applying the proposed GASP to a family of transmuted probability distributions. For illustration purposes, a real data set for fatigue fracture stress is analyzed using MLE estimates of AGTransmuted-Exponential distribution to demonstrate the implementation of the proposed sampling plan.