Advanced Quality Management / Six Sigma
With analytical Sigma metrics, when it comes to bias, negative is always negative
The analytical Sigma metric equation subtracts bias from the allowable total error (TEa.). But what happens when the bias is negative?
With analytical Sigma metrics, when it comes to bias, negative is always negative
October 2026
Sten Westgard, MS
I came across a recent study of analytical Sigma metrics:
Analisis Quality Control Pemeriksaan Albumin Dan ALT (alanine aminotransferase) menggunakan Grafik Levey-Jennings Dan Six Sigma. [Translation: Analysis of Quality Control for Albumin and ALT (Alanine Aminotransferase) Testing Using Levey-Jennings Charts and Six Sigma]. Jurnal Insan Cendekia Volume 13 No.2 September 2026. Najwa Aulya Nur Fatimah Azzahro, Aji Bagus Widyantara, Titin Aryani.
https://ejournal.itskesicme.ac.id/index.php/jic/article/view/1640
This is a very small study, from the Yogyakarta City General Hospital, Indonesia, on an instrument I've never heard of before - the Pictus 500 - looking at just one level for 2 analyltes, albumin and ALT.
The study goes to great length to collect bias data, and it determined there was negative bias.
Here is the data:
Albumin 10% TEa, -4.26% Bias, 4.56% CV, with a calculated analytical Sigma metric of 3.13.
ALT 20% TEa, -5.36% Bias, 4.22% CV, with a calculated analytical Sigma metric of 6.01.
Do you see the mistake?
The negative bias here is being used in the analytical Sigma metric equation, like so:
Analytical Sigma metric of Albumin = (10 - (-4.26)) / 4.56 = (10 + 4.26) / 4.56 = 14.26 / 4.56 = 3.13 Sigma
Analytical Sigma metric of ALT = (20 - (-5.36)) / 4.22 = (20 + 5.36) / 4.22 = 25.36 / 4.22 = 6.01 Sigma
The double negative turns the bias into a positive. Thus, the bias is adding to the allowable total error, making the allowable total error larger, and ultimately increasing the analytical Sigma metric.
In truth, when the bias is included in the equation, it's the absolute value of the bias that should be subtracted. Bias should always be negative. This means the equation is always assuming the worst-case scenario.
Here are the correct calculations:
CORRECT Analytical Sigma metric of Albumin = (10 - |-4.26|) / 4.56 = (10 - 4.26) / 4.56 = 5.74 / 4.56 = 1.26 Sigma
CORRECT Analytical Sigma metric of ALT = (20 - |-5.36|) / 4.22 = (20 - 5.36) / 4.22 = 14.64 / 4.22 = 3.47 Sigma
In the defense of the authors' mistake, there are descriptions of the Sigma metric out there that show the bias without absolute value signs, but usually in that display, the text accompanying the equation notes that the absolute value of the bias should be used.
From 3.13 Sigma down to 1.26 Sigma, that's the barely minimum acceptable Sigma down to an unacceptable performance.
From 6.01 Sigma down to 3.47 Sigma, that's world class quality down to the bare minimum performance.
The treatment of bias has a huge impact.
What's even more concerning, the goals being used here are from 1992 CLIA specifications. The 2025 CLIA goals are smaller, even harder to hit: Albumin 8% and ALT 15%. If we ran the numbers using these modern goals, the Sigma metrics will be even lower.
The final verdict on these two Pictus 500 methods will be that neither is acceptable. More data from more levels, more tests, and more labs is needed to determine whether or not this is an unusual outlier or a reflection of typical performance.