A new mixed repetitive group sampling plan based on the process capability index for product acceptance

Abstract

Purpose The purpose of this paper is to propose a new mixed repetitive group sampling (RGS) plan based on the process capability index, Cpk, where the quality characteristics of interest follow the normal distribution with unknown mean and unknown variance. Tables are constructed to determine the optimal parameters for practical applications for both symmetric and asymmetric fraction non-conforming cases. The advantages of this proposed mixed sampling plan are also discussed. The proposed sampling plan is also compared with other existing sampling plans. Design/methodology/approach In order to determine the optimal parameters of the proposed mixed RGS plan based on Cpk, the authors constructed tables for various combinations of acceptable and limiting quality levels (LQLs). For constructing tables, the authors followed the approach of two points on the operating characteristic (OC) curve. The optimal problem is formulated as a non-linear programming where the objective function to be minimized is the average sample number (ASN) and the constraints are related to lot acceptance probabilities at acceptable quality level and LQL under the OC curve. Findings The proposed mixed RGS plan will be a new addition to the literature of acceptance sampling. It is shown that the proposed mixed plan involves minimum ASN with desired protection to both producers and consumers compared to other existing sampling plans. The practical application of the proposed mixed sampling plan is also explained with an illustrative real-time example. Originality/value In this paper, the authors propose a new mixed RGS plan based on the process capability index Cpk, where the quality characteristic of interest follows the normal distribution with unknown mean and unknown variance. Tables are constructed to determine the optimal parameters for practical applications. The proposed mixed sampling plan can be used in all production industries. This kind of mixed RGS plan is not available in the literature.