Determining Sample Size for Estimating Process Defective Rate in Case of a Defect Counting Metric

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 defect counting data, the usual formula taught is about estimating the mean number of defects per unit and not the proportion of defective units (i.e., the defective rate). This paper elaborates a formula and derived tables for calculating the sample size required to achieve the needed statistical precision on the defective rate when working with a defect counting metric. Reversely, the precision obtained for a given sample size is calculated. The results are then compared to those for binary data and it is suggested that the sample size calculation for binary data is worth to be considered as an acceptable easier-to-use alternative. The challenge to obtain decent precisions due to the sample size requirements when operating at low defective rates is also highlighted