The 1.5 Sigma Shift Story

One of the greatest criticisms that have been mounted against the six sigma methodology is the fact that there is a possibility that the entire system is built on fudged numbers. Statisticians have claimed that the name six sigma is misleading. Here are the reasons why:

3.4 Defects Per Million or 2 Defects Per Billion

The statistical term Six Sigma actually refers to a process in which there will be 2 defects per billion times the process is run. However, the definition of Six Sigma accepted by modern day practitioners is a much easier to follow, 3.4 defects per million. Although even achieving efficiency of 3.4 defects per million, makes the process achieve near zero and therefore negligible defects, the statistical name 6 sigma is misleading. The values 3.4 defects per million, in reality, correspond to 4.5 sigma levels. The balance is accounted for by the 1.5 sigma shift.

Long Term vs. Short Term

The logic behind the 1.5 sigma shift is rooted in empirical studies. Empirical studies have shown that processes tend to fare better in the short term than they actually do in the long term. This is because in the short term, there is only normal process variation that needs to be dealt with. However in the long term cases of special process variation also occur. This results in the process performing at 6 sigma levels in the short run but at 4.5 sigma levels in the long run.

Long Term Dynamic Mean Variation

The long term variation in the process variation is accounted for by one of the two reasons:

  • Variation in the process mean over time
  • Increase in the standard deviation of the process over time

As a result of either of the above reasons, or a combination of both, the process fails to meet its Six Sigma objectives. This phenomenon is called long term dynamic mean variation.

Empirical Studies at Motorola

Now, we know that the Six Sigma criteria are not met because of long term dynamic mean variation. But how do we know that we need to remove 1.5 sigma from both sides of the normal curve. Well, it isn’t a statistical reality but just an industry convention.

Motorola was the pioneer of Six Sigma methodology worldwide. They have made empirical studies about the processes that they have improved and concluded that a 1.5 sigma shift occurs. While many statisticians have called this 1.5 sigma shift arbitrary, the industry wants to go the Motorola Way and 3.4 defects per million which define 4.5 Sigma have become an industry wide accepted definition of a Six Sigma process.


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