Last Updated on 13 September 2023

If you want to reach six sigma level (or even five sigma or any of the other levels), you need to know where you currently are, and set yourself targets. For this you need a way to calculate your sigma level, as unfortunately it’s unlikely that it will be written on the side of your machinery!

The easiest way to calculate it is usually through DPMO, or Defects per Million Opportunities.

## What is DPMO?

DPMO is the number of Defects, or things that have gone wrong to a level unacceptable for your customer, for each million opportunities for things to go wrong. For simple products, there may only be a few opportunities per unit such as 5, but for complicated products it could go into the tens or even hundreds! For these modern complex operations you therefore need to get a very high yield for a product that is acceptable to your customers.

Your opportunities are therefore just the number of units produced multiplied by the number of opportunities for error per unit.

## Calculating Sigma level

Once you have your DPMO, you can then calculate your Sigma level. This generally assumes that your data follows a standard normal distribution, which most will

The most common method is usually to use a Sigma level lookup table. From this you can simply go down it until you find the DPMO that you have and this will give you the Sigma level. You can also usually calculate it using Cpk or yield.

By using the same table, you can also find out your yield or DPMO for various sigma levels, which is useful for setting your organizational targets.

## Six Sigma Shift

When you calculate your Sigma level, it is usually the short term quality level that you are calculating. It is generally assumed that over a long period of time, the Sigma level will shift by 1.5, so to calculatate your Long term Sigma level from your Short term sigma level, you need to add 1.5. It’s always important that when you’re describing what you’re aiming for, that you make it clear which of these you’re using. If it isn’t mentioned, it’s often assumed that it’s the long term level that you’re looking at, as that is where the ‘six sigma’ target comes from.

Another method of calculating the Sigma level is to use Excel.

I’ve made a full page on this that goes into more detail, but there are some excel formulas that give you the calculation very easily, without having to resort to lookup tables. As you will generally be keeping track of your quality data in a spreadsheet, this gives you an easy way to have your sigma level calculations in the same place, giving you real time updates on your progress. The main calculation is the NORMSINV() and NORMSDIST() formulas.

DPMO = NORMSDIST (1.5 – σ) x 1,000,000

Sigma level = ABS (NORMSINV(DPMO / 1,000,000)) + 1.5

This gives you a nice quick way of calculating Sigma level.

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