Design and Construction of a Variables Repetitive Group Sampling Plan for Unilateral Specification Limit

Abstract

This paper attempts to develop a repetitive group sampling (RGS) plan by variables inspection for controlling the process fraction defective or the number of nonconformities when the quality characteristic follows a normal distribution and has only the lower or upper specification limit. The proposed sampling plan is derived by the exact sampling distribution rather than the approximation approach. The plan parameters are solved by a nonlinear optimization model which minimizes the average sample number required for inspection and fulfills the classical two-point conditions on the operating characteristic (OC) curve. The efficiency of the proposed variables RGS is examined and also compared with the existing variables single sampling plan in terms of the sample size required for inspection. The results indicate that the proposed variables RGS plan could significantly reduce samples required for inspection compared to the traditional variables single sampling plan.

Keywords:

• Acceptance sampling
• Average sample number
• Lot sentencing
• Operating characteristic curve

Mathematics Subject Classification:

• Primary 62F03
• Secondary 62P30

Acknowledgments

The earlier version of this paper was presented at the 2012 Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modeling (APARM 2012) in Nanjing, China. This work was partially supported by the National Science Council of Taiwan under Grant No. NSC 100-2628-E-007-035-MY3 and the Ministry of Education, Taiwan under Grant No. 100N2073E1.