The Sigma Shift

Hello colleagues and welcome to week-3 of the Weekly Lean Series in 2021.

Today we are going to discuss a phenomena, namely the Sigma Shift . Sigma shift is a phenomenon and a standard calculation metric devised in the journey of Motorola in their pursuit of perfection via organizing operational excellence model around the Six Sigma methodology.

Before diving too much into this let us first see the main table used in understanding sigma levels of a process. Sometimes these levels also describe the level of an organization as well. Traditionally we use the 6-sigma level to explain a process so fit into the customer specifications that it has the possibility to violate these specifications only 3.4 times in a million opportunities, thus DPMO. Similarly as the sigma level is lower this possibility increases to 691.462 DPMO for a process at 1 sigma level.

However when you crunch the numbers from a Z table you will see that a normal distribution that is +/- 6 standard deviations actually has 2 defects per billion opportunities vs 3.4 DPMO Checking another sigma level , say +/- 3 standard deviations, you will see that 66807 DPMO is stated in our table whereas Z table states that it is 2700 . So what is going on , is there a problem with Motorola's table?

The difference comes from the fact that Motorola , by observing numerous data from its processes in the past years, has come to a conclusion that processes shift in the long term by 1.5 sigma from the target. Therefore a process achieving 3 sigma level will result in 99.73% success rate in the short term but this will erode to 93.3 % in the long term. Similarly your process achieving 6 sigma actually is capable of 2 defects per billion but this will erode to 3.4 DPMO in time.

When you analyze a process in short term there are certain factors ignored that would normally add additional variation. All processes are designed to meet the specification limits but as a law of thermodynamics , entropy enters and variation plays its role either shifting the process mean or increasing standard deviation due to reasons like random assignable causes which are not included in the short term data. Thus this 1.5 sigma shift will ensure that the process can meets targets in the long term.

So your Z tables are fine and don't check your calculations as the long term entropy is something to consider in our calculations. Take care and see you in the next part :)