The Influence of Sample Size on Long-Term Performance of a 6σ Process

• Published in: Processes 2023-03, Vol.11 (3), p.779
• Main Authors: Boroiu, Andrei Alexandru, Titu, Aurel Mihail, Boroiu, Alexandru, Dragomir, Mihai, Pop, Alina Bianca, Titu, Stefan
• Format: Article
• Language: English
• Subjects: Control limits; Lean manufacturing; Mathematical analysis; Quality improvement; Sample size; Six Sigma
• ISSN: 2227-9717; 2227-9717
• DOI: 10.3390/pr11030779

There are many criticisms for the association between the Six Sigma concept and the two statistical metrics associated to 6σ processes: 1.5σ shift for maximum deviation and 3.4 PPM non-conformities for the long-term performance. As a result, the paper aims to carry out an analysis of this problem, and the first result obtained is that a stable process can reach a maximum drift, but its value depends on the volume of the sample. It is also highlighted that, using only the criterion “values outside the control limits” for monitoring stability through the Xbar chart, a minimum value can be calculated for the long-term performance of a process depending on the sample size. The main conclusion resulting from the calculations is that, in the case of a 6σ process, the long-term performance is much better than the established value of 3400 PPB: For small volume samples of two pieces it is below 700 PPB, for three pieces it is below 200 PPB, and for samples with a volume greater than or equal to four pieces the performance already reaches values below 100 PPB! So, the long-term performance of 6σ processes is certainly even better than the known value of 3.4 PPM.