Statistical Six Sigma Definition

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hat does it mean to be "Six Sigma"? Six Sigma at many organizations simply means a measure of quality that strives for near perfection. But the statistical implications of a Six Sigma program go well beyond the qualitative eradication of customer-perceptible defects. It's a methodology that is well rooted in mathematics and statistics.

The objective of Six Sigma Quality is to reduce process output variation so that on a long term basis, which is the customer's aggregate experience with our process over time, this will result in no more than 3.4 defect Parts Per Million (PPM) opportunities (or 3.4 Defects Per Million Opportunities – DPMO). For a process with only one specification limit (Upper or Lower), this results in six process standard deviations between the mean of the process and the customer's specification limit (hence, 6 Sigma). For a process with two specification limits (Upper and Lower), this translates to slightly more than six process standard deviations between the mean and each specification limit such that the total defect rate corresponds to equivalent of six process standard deviations.

Many processes are prone to being influenced by special and/or assignable causes that impact the overall performance of the process relative to the customer's specification. That is, the overall performance of our process as the customer views it might be 3.4 DPMO (corresponding to Long Term performance of 4.5 Sigma). However, our process could indeed be capable of producing a near perfect output (Short Term capability – also known as process entitlement – of 6 Sigma). The difference between the "best" a process can be, measured by Short Term process capability, and the customer's aggregate experience (Long Term capability) is known as Shift depicted as Z_shift or s_shift. For a "typical" process, the value of shift is 1.5; therefore, when one hears about "6 Sigma," inherent in that statement is that the short term capability of the process is 6, the long term capability is 4.5 (3.4 DPMO – what the customer sees) with an assumed shift of 1.5. Typically, when reference is given using DPMO, it denotes the Long Term capability of the process, which is the customer's experience. The role of the Six Sigma professional is to quantify the process performance (Short Term and Long Term capability) and based on the true process entitlement and process shift, establish the right strategy to reach the established performance objective

As the process sigma value increases from zero to six, the variation of the process around the mean value decreases. With a high enough value of process sigma, the process approaches zero variation and is known as 'zero defects.'

Statistical Take Away
Decrease your process variation (remember variance is the square of your process standard deviation) in order to increase your process sigma. The end result is greater customer satisfaction and lower costs.

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