2 ways to calculate Six Sigma (for Continuous and Discrete data)

2 ways to calculate Six Sigma (for Continuous and Discrete data)

Learn Process Sigma calculation in simple easy steps without the need of using any calculator, you can use Excel to do all your calculations. Process Sigma is also known as Six Sigma and both the terms are same.

Six Sigma calculation is the first thing that every six sigma practitioner or student should understand and know how to calculate. Learn the fundamentals here, how to calculate sigma level manually and so easily without the help of any tool like Minitab. I am a veteran as a Black Belt and I can tell you that most of the Black Belts don’t know how to calculate it manually, they tend to depend on some application.

First of all the most basic thing is that sigma level is calculated differently for discrete and continuous type of data.

Quick Recap – Understand your data type

Quick Excel method to calculate Process sigma for discrete data

Defects per million opportunities (DPMO) of a process is the total no. of defects divided by total defect opportunities, multiplied by one million. Synonymous with PPM.

Defects : It is the failure of the process as per specification. It can be in a form of wrong information, wrong opening of call , no closing …. Etc . Denoted by d

Unit (U) –The number of parts, sub-assemblies, assemblies, or systems inspected or tested.

Opportunity (O) –A characteristic you inspect or test. It is the maximum nos. of defects possible in one unit.

Defect (D) –Anything that results in customer dissatisfaction. Anything that results in a non-conformance.

Defects per opportunity – DPO: (D/(U * O))

Defects per million opportunity – DPMO : ( DPO * 1000,000)

1.Number of Units processed

2. Number of Opportunities for error per Unit

3.Total number of Defects

4.Solve for Defects Per Opportunity
DPO = ( D )/ ( U *O )

5.Convert DPO to DPMO
DPMO = DPO * 1,000,000

6.Look up Process Sigma in conversion table

Process Sigma – When my data is discrete

Let us use this quick Excel method with an example.

Units(U) = 3

Opportunity(O) = 5

Defects(D) = 5

So, our DPO would be = 5 / (5*3) = 0.33

Now use the Excel formula =-normsinv(.33)+1.5 for short term sigma.

You will get a value of 1.93, this is the process sigma and you can cross check the sigma table in the previous example. The value is same. This will save you time and effort.

Process Sigma – When my data is Continuous

  • To calculate Sigma for continuous data, we need to calculate Cpk. You can check Process Capability section for more details
  • Cpk compares product specifications relative to centre () of the process
  • Similar to Cp in that it uses the standard deviation of the process, but does not need to have process centered to specification limits.

Let us understand calculating process sigma for continuous data with some examples.

Example 1:

When we have both USL(Upper Specification Limit) and LSL(Lower Specification Limit)

Let us assume the plant is manufacturing an aluminum rod and the LSL is 80 cm and the USL is 80.8 cm. When the lots were inspected the mean or average length found was 80.2 cm and sigma(Standard Deviation) was 0.05.

So we have following data with us

  • LSL = 80 cm
  • USL = 80.8 cm
  • Mean = 80.2 cm
  • SD(sigma) = 0.05

When we use the above mentioned formulas for Cpu and Cpl, we will have:

Cpu = 4 and Cpl = 1.33

So, our Cpk would be the smaller one and that is 1.33

Hence, Process Sigma = 3 * 1.33 = 4

Example 2:

When we have only USL(Upper Specification Limit) or LSL(Lower Specification Limit)

Let us assume that a task needs to be completed within 400 Sec as per the customer, so the USL is 400 Sec. There is no lower limit set by the customer so there is no LSL.

The process is working with a mean of 380 Sec and sigma(Standard Deviation) of 15.

So we have following data with us

  • LUSL = 400 Sec
  • Mean = 380 Sec
  • SD(sigma) = 15

Cpu will be Cpk since there is no Cpl.

Cpk = 0.44

Hence, Process Sigma = 3 * 0.44 = 1.33

Please note : Process Sigma can take negative value as well, there is nothing wrong with that.

I hope you have understood the above concept and if you want to learn more such tools then go for a Six Sigma course from Simplilearn. The course is aligned to IASSC and ASQ exam, integrates lean and DMAIC methodologies using case studies and real-life examples.

There is another good online Six Sigma Green Belt course from Coursera. This course is from University System of Georgia and is well recognized.

If you want to learn new age data science techniques, then one good starting point is Data Science course from Simplilearn. Data Science is emerging very fast and early movers will always have advantage.


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