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Developing a sampling plan based on Cpk—unknown variance



Common acceptance sampling plans for variables do not take into account the process performance while determining the sample size needed. An attempt to overcome this gap was suggested by Negrin et al. (Quality Eng. 2009; 21: 306–318), where a sampling plan based on the Cpk index was developed. The plan is a multistage acceptance sampling plan based on Cpk for variables taken as a random sample from a lot of size N having (approximately) normal distribution with a known variance. In the current research, we relax the assumption of a known variance and develop a Cpk sampling plan based on unknown variance. We develop a sample size model and update the acceptance/rejection criteria of the previous sampling plan to the new, more realistic model with unknown variance. In addition we develop the operational characteristic curve (OCC). The sampling plan is compared with the commonly used plan MIL-STD-414 (Sampling Procedures and Tables for Inspection by Variables for Percent Defective. Department of Defense: Washington, DC, 1957) and it is found (via simulations) that the Cpk sampling plan has a smaller probability of accepting defective lots and the required sample size needed is found to be smaller for large lots. In addition, a comparison is made between the two OCCs and it is found that the OCC developed for the Cpk sampling plan shows a higher accuracy (in an order of magnitude) in classifying lots correctly. Copyright © 2010 John Wiley & Sons, Ltd.