Westgard QC, Inc. : The Six Sigma Calculators

The Six Sigma Calculators

NOTE: This page only works on browsers that support Javascript!

[Note: This Six Sigma Calculator is an extension of the lesson From Method Validation to Six Sigma: Translating Method Performance Claims into Sigma Metrics. This article assumes that you have read that lesson first, and that you are also familiar with the concepts of QC Design, Method Validation, and Six Sigma. If you aren't, follow the link provided.]

DPM (Defects Per Million) Calculator

Here you can calculate the Sigma-metric by counting the number of Defects in a sample.
Note that this calculator "rounds up" - to the nearest Sigma-Metric on the table on this website.

Enter the number of Defects Observed:
Enter the size of the sample: (how many total results were examined)
Here are your Defects Per Million: Here is your Sigma-Metric:

Note also that if you know your Defect/Error rate as a percentage, you can enter it here with the sample size of 100 (i.e. a defect rate of 2% would be entered "2" in the defects observed, and "100" in the size of the sample).

Process Design Calculator

Here you can calculate your Sigma-metric by analysis of variance measurements.

Enter the Quality Requirement or Tolerance Limit (in %): (If you don't know, look it up below)
Observed Bias (as a %): (If you don't know, start with 0)
Observed CV (as a %): (If you don't know, find out)

QC Design Calculator (Critical Systematic Error)

Here you can calculate the size of the error your QC must detect.

Enter the Quality Requirement or Tolerance Limit (in %): (If you don't know, look it up below)
Observed Bias (as a %): (If you don't know, start with 0)
Observed CV (as a %): (If you don't know, find out)

Limitations

These Javascript calculators are for demonstration purposes only. In particular, if you enter nonsensical numbers, they will return nonsense. Entering 0 for Defects Observed, Sample Size, Quality Required, Observed CV will give you useless answers. More robust Six Sigma calculators are available upon request.

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Benchmarking: How do your processes compare?

The following Sigma metrics are drawn from Nevalainen D, Berte L, Kraft C, Leigh E, Morgan T. Evaluating laboratory performance on quality indicators with the six sigma scale. Arch Pathol Lab Med 2000;124:516-519.

Q-Probe QUALITY INDICATOR	% ERROR	DPM	SIGMA*
Order accuracy	1.8 %	18,000	3.60
Duplicate test orders	1.52	15,200	3.65
Wristband errors (not banded)	0.65	6,500	4.00
TDM timing errors	24.4	244,000	2.20
Hematology specimen acceptability	0.38	3,800	4.15
Chemistry specimen acceptability	0.30	3,000	4.25
Surgical pathology specimen accessioning	3.4	34,000	3.30
Cytology specimen adequacy	7.32	73,700	2.95
Laboratory proficiency testing	0.9	9,000	3.85
Surg path froz sect diagnostic discordance	1.7	17,000	3.60
PAP smear rescreening false negatives	2.4	24,000	3.45
Reporting errors	0.0477	477	4.80

*Conversion using table with allowance for 1.5s shift

As shown by the variety of preanalytic, analytic, and postanalytic processes in this table, the approach of using outcome measures can be applied to virtually any process. The observed error rates for several of these processes are in the 3.0% to 0.3% range, which translates to typical sigma levels of 3 to 4. Even analytical performance, as estimated from proficiency testing data, is only at the 3.85 sigma level. The best process is "reporting errors" which has a sigma metric of 4.80. No process achieves the six sigma goal.

Some rules of thumb:

3-Sigma performance is considered the minimum for any industrial process.
Typical performance of business and industry processes is considered to be around 4-Sigma.
The first goal of a Six Sigma project in business and industry is usually to improve from 4-Sigma to 5-Sigma. This is in fact a very significant improvement: a 100-fold reduction in defects in the short term!
Some processes never reach 6-Sigma. But reaching 5-Sigma may be good enough. In some cases, the process can be reengineered to acheive 6-Sigma performance.