Determining Sample Size for Estimating Process Defective Rate in Case of a Continuous Metric
19 Pages Posted: 28 Mar 2022 Last revised: 29 Aug 2022
Date Written: April 10, 2022
Abstract
As part of the Measure phase of a Six Sigma (DMAIC) project, it is key to determine the sample size appropriate given the statistical precision needed on the estimation of the process capability (defined here as the expected proportion of defective units). Six Sigma practitioners are generally taught to use either some rule of thumb (skipping so the precision requirement) or a sample size formula allowing to specify the required precision. While such a formula is provided for binary data, when dealing with continuous data, the usual formula taught is about estimating the mean and not the defective rate. Other alternative approaches are about calculating the sample size based on precision on process capability indexes designed for manufacturing industry. However, these technical indexes are often not relevant for most users and managers not working in specific production environments. This paper elaborates solutions for calculating the sample size required to achieve the needed statistical precision on the defective rate when working with a continuous metric in both cases of one and two specification limits. Reversely, the precision obtained for a given sample size is calculated. The challenge to assess high Sigma performance levels because of the required sample size is also highlighted.
Keywords: quality management, six sigma, process capability, sample size, statistical theory
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