Impact of six sigma estimated using the Schmidt-Launsbyn vs. the Westgard equation in the Spanish type I EQA program

Six sigma methodology (SM) measures process performance using defects per million opportunities (DPMOs). SM has traditionally used the Westgard equation (WM), by which DPMOs are calculated indirectly. An alternative for directly calculate DPMOs is the Z-transformation method in combination with the Schmidt-Launsbyn equation. The implementation of SM in External Quality Assurance (EQA) programs is limited, which hampers their evaluation. A study was conducted to compare SM values obtained with the two equations.

Sigma value (SV) was estimated based on data from a Type I EQA Program (SCR-EQA-SEQC^ML) using two methods: the Westgard equation, and the Z-transformation + Schmidt-Launsbyn method (S-LM). A comparison of the SVs obtained with the two methods was performed.

SVs were calculated from 949 values provided by the EQA program. The results indicate that WM underestimates SV, as compared to S-LM, independently of whether outliers were removed (2.9) or not (1.9). This underestimation occurs as a result of treatment bias rather than imprecision.

Unlike MW, S-LM adjusts for bias, thereby preventing negative SVs. S-LM is not as influenced by outliers as MW and yields more robust SV estimates in EQA programs. This guarantees a more precise evaluation of results and classification of method/system performance.