What is Sigma and Why is it Six Sigma?

Mean is the arithmetic average of a process data set.
Central tendency is the tendency of data to be around this mean.
Standard Deviation (also known as Sigma or σ) determines the spread around this mean/central tendency.

The more number of standard deviations between process average and acceptable process limits fits, the less likely that the process performs beyond the acceptable process limits, and it causes a defect. This is the reason why a 6σ (Six Sigma) process performs better than 1σ, 2σ, 3σ, 4σ, 5σ processes.

Obviously 7 or more σ processes are even better than a 6σ (Six Sigma) process, and yet throughout the evaluation and history of Six Sigma process, the practitioners gained the belief that a 6σ process is good enough to be reliable in almost all major situations except some systems whose defects can cause unrepairable consequences.


Six Sigma stands for 6 standard deviations (6σ) between avarage and acceptable limits


LSL and USL stand for “Lower Specification Limit” and “Upper Specification Limit” respectively. Specification Limits are derived from the customer requirements, and they specify the minimum and maximum acceptable limits of a process.

For instance in a car manufacturing system the desired average length (Mean length) of car door can be 1.37185 meter. In order to smoothly assemble the door into the car, LSL can be 1.37179 meter, and USL can be 1.37191 meter. To reach a 6σ quality level in such a process, the standard deviation of car door length must be at most 0.00001 meter around the mean length.

Sigma is also the capability of the process to produce defect free work. Higher the capability, lower the defects.


Processes in various Sigma Levels


In the above figure, the red curve indicates a 2σ level of performance where we observe that its peak is very low (fewer outputs are around the desired average) and the variation is from extreme left to extreme right of the figure. If the process improves from 2σ to 3σ (green curve), you will observe that the process variation reduces and the process has a larger peak (more outputs are around the desired average, but a different average than red curve). As the process performance increases from 3σ to 6σ (blue curve), the process becomes centered between the upper and lower specification limits and does not have much variation. Here with blue curve the majority of process outputs are around the desired average. This is why it is good and it causes less defects beyond the lower and upper specification limits.


Sigma Level vs DPMO Defects per Million Opportunities


In the above table, you will observe that as the Sigma level increase the Defects decrease. For example, for a 2σ process the Defects are as high as 308,537 in one million opportunities. Similarly, for a 6σ process the Defects is as low as 3.4 in one million opportunities. The 2σ performance level will have more defects than a system in 6σ performance level as the standard deviation for a 2σ process is much larger than the standard deviation for a 6σ process.

Can we have any process which has 6σ level of performance?
The answer is yes. Pharmaceutical Companies, Airline Manufacturing Organizations, Automobile Manufacturers, among others are bound to work at a sigma level which is either 6σ or more than that. If they are not able to perform at this efficiency, the organization cannot exist. Think about it, you are in the air, 5000 feet above the ground, flying in a Boeing 777 Aircraft and suddenly a nut-bolt in the wing of the plane loosens (probably due to manufacturing defect) making it difficult for the pilot to steer the flight! This is the only reason why defects are not welcome and organizations try to achieve higher Sigma levels.


Six Sigma vs DPMO Examples


In the above examples,
  • Sigma indicates the Sigma level.
  • Spelling indicates the total spelling errors.
  • Money indicates the amount of fine/indebtedness that can occur due to the misspellings.
  • Time indicates the total time it takes to correct those misspellings.
  • DPMO indicates the total Defects in One Million Opportunities.
We can clearly observe that as the Sigma Level increase, the defects (misspellings) decrease, the indebtedness reduce and the time for rework also reduces, thus it reduces the DPMO-Defects per Million Opportunities.



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