Six Sigma

SixSigma is a ProcessImprovement methodology promoted by Motorola. The method was designed for ManufacturingEngineering? situations, where defects are caused by ProcessParameters? varying too much.

The method is very useful for checking if a manufacturing process is capable of producing a design, because it compares the process variability to the design requirements. It is also useful for adjusting manufacturing processes to minimize their defect rates.

However, it is often used in other situations (like processing paperwork), where defects either exist or don't exist, and the reason for the underlying variability is unknown.

I have seen SixSigma lumped together with TotalQualityManagement. Are they very much related?

example see http://www.plant-maintenance.com/articles/Mixing_Maintenance_Methods.pdf

The name SixSigma refers to a metric for predicting defect rates.

In many manufacturing processes, important parameters (like temperature of a furnace, or length of machined part) can be measured. This data can be analyzed statistically. For example, the StandardDeviation can be calculated. Sigma is the symbol for StandardDeviation. The higher the StandardDeviation, the more the parameter varies -- and the less likely we are to achieve the CustomerRequirement?s.

The StandardDeviation can be estimated, even with very little data. For example, if 3 randomly chosen parts are 8.000 inches long, 8.005 inches long, and 8.010 inches long, then the average is 8.005 inches, and the SampleStandardDeviation? is 0.005 inches. (Yes, I really did get out my calculator for that!) Using just 3 data points makes this a very rough estimate. You need at least 30 data points for a statistically "valid" estimate.

The CustomerRequirement?s can often be translated (more or less painfully) into a tolerance for the parameter being measured. For example, if the furnace temperature is 2 Celsius degrees above average, a coating might be too thick. Or, the part must be between 7.980 inches and 8.020 inches long in order to fit in the next assembly. The tighter the tolerances, the less likely we are to achieve the CustomerRequirement?s.

The metric used in SixSigma calculations is: Abs(ClosestSpecificationLimit? - ProcessAverage?) / StandardDeviation

For example: (8.020 inches - 8.005 inches) / (0.005 inches)

Equals: (0.015 inches) / (0.005 inches)

Equals: 3 Sigma

A higher SigmaNumber? is better.

One of the first lessons of the SixSigma methodology is to CenterTheProcess. In this example, we want to be equally likely to make parts that are too short or too long. Sometimes centering the process is a bad idea. The CenterTheProcess page has counter-examples.

If we (somehow) change the ProcessAverage? to 8.000 inches, we get (8.020 inches - 8.000 inches) / (0.005 inches)

Equals: (0.020 inches) / (0.005 inches)

Equals: 4 Sigma

Because this StandardDeviation was estimated from just 3 data points, we don't really know whether the process was already centered at 8.000 inches. Maybe it was a fluke that the 3 data points were on the same side of 8.000 inches. Making adjustments based on too little data is actually counter-productive -- though it might make sense to double-check the calibration of the part cutting machine.

On a good day, a 1 Sigma process has a 1/3 chance of producing a defect in any given opportunity. A 2 Sigma process has a 5% defect rate (on a good day). A 3 Sigma process has a 0.3% defect rate (on a good day), etc.

However, many days are not good days. Motorola assumes that the process can shift by 1.5 Sigma before someone notices the problem and re-centers the process. So a process that is at 2 Sigma on a good day may be at 0.5 Sigma on a bad day (and have a 2/3 defect rate). A process that is at 1 Sigma on a good day can have a 100% defect rate on a bad day!

The goal of the SixSigma methodology is to reduce the variation and/or loosen the CustomerRequirement?s enough to achieve a 6 Sigma quality level. A 6 Sigma process has 3 defects per 1,000,000 opportunities (even on a bad day).

But 0 sigma means that the average is right at one of the spec limits, so half the parts are in spec and half out. 0.5 sigma would mean better than half the parts are in spec, not 2/3 out.

No, 0 sigma means that all of the parts are more than 0 sigma away from the mean - in either direction. It is like having the upper and lower spec limits equal the mean exactly.

Because many managers want to apply this method, even in non-manufacturing areas that can't measure their process variation, there are tables for converting defect rates into Sigma values.

Most of Discussion and below moved to SixSigmaDiscussion, except for the following clarification:

When a company says it is using SixSigma, it is referring to the SixSigma methodology for defect reduction, which includes several statistical tools in addition to the metric described above. But, when a company claims that a process has reached SixSigma, it is referring to six standard deviations, as calculated above.

The SixSigma methodology for defect reduction is known by the acronym DMAIC: Define Measure Analyze Improve Control. There are many books on Six Sigma which describe the methodology and tools (I won't list any here; just search Amazon, bookpool, or your favorite bookseller). I have found so far only one published book specifically on "Six Sigma Software Development", which seemed to be more of an overview of Six Sigma with brief references to software, than a thorough discussion of the considerations of applying Six Sigma tools to software process improvement. A better resource is the Measurement and Analysis program at the SoftwareEngineeringInstitute (http://www.sei.cmu.edu/sema/). Their team includes a Six Sigma black belt, Jeannine Siviy, who is leading their effort to explore applying Six Sigma for software.

See SixSigmaDiscussion for thoughts on the relative merits or demerits of applying Six Sigma for software ;)

KarenSmiley, 8/14/2003

Resources related to SixSigma

Beginner

Newbie material -> http://www.isixsigma.com/library/content/six-sigma-newbie.asp

ICT related material and links -> http://www.isixsigma.com/bp/it/ and http://www.softwaresixsigma.com/SixSigma_Main_SixSigma.htm

Other

QuickWins and Reducing Cyle time http://www.isixsigma.com/library/content/c031110a.asp

CategoryMethodology CategoryManufacturing CategoryStatistics