Articles

Revision Proposal of the Number of Distinct Categories Definition and Acceptance Criteria for Measurement System Validation

Author : Youri Buffe

September 23, 2022

Abstract :

%GRR and Number of Distinct Categories (NDC) are widely used as measurement system capability indicators. However, the usually accepted calculation formula of the NDC is assigned a coefficient whose origin have led to the coexistence of two different and misleading interpretations of the NDC. We recommend to remove this coefficient in order to stick to the measurement system resolution definition or equivalent signal-to-noise concept. We also propose a realignment of the %GRR and NDC acceptance thresholds.

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

Author : Youri Buffe

May 3, 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 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.

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

Author : Youri Buffe

March 28, 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.

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