Q 530. Explain the concept of Six Sigma performance with the help of a Bell Curve?

 

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How to curb defects and boost daily production is the key to what six sigma offers by process improvements, delays elimination and fixing other aspects of a production process.

 

Essentially, six sigma is a statistical management application used to produce processes having lowest defects.

 

The mathematical formula to calculate the sigma level is as follows:

 

“(Opportunities-Defects)/Opportunities x 10”

 

Theoretically the output for six sigma level ranges from 1 to 6 as follows:

The sigma term is used to denote the sigma level in any given part of a process and state the defects that occur at that particular sigma level for that process. Any process that operates at sigma level-6 is deem to be perfect with regard to statistics. As such, it has only 3.4 DPMO (Defects Per Million Opportunities) whereby it’s accuracy is at 99.99966% of operating capacity.

 

A process is statistically differentiated at a sigma level-5 with a sigma level-6 in relation to the presence of number of defects involved.

 

In a +/- sigma level-1.5, the data portion will be 0.4332. Note that as the level of 6 sigma falls, the defect value may either fall or increase as well. It is important to note that errors and expenses rises as the level of sigma falls.

 

Under specific conditions the team lead for enhancing a process, may encounter a data distribution for defect which are positive and skewed, and as such he need to take corrective actions based on the defects involved. Subsequently, the baseline performance is an imperative factor to be used to be taken into account to be able to shift from defects to acting upon improvement.

 

Based on the above illustrations the sigma level is derived based on the number of standard deviation that any process has in relation to the mean and customer specifications. Hence, in an attempt to have more standard deviation with the mean and customer specifications at intervals, there will be a minimizing amount of defects in the process and thus increasing level of sigma that will eventually benefit the customer to its expectations.

 

The probability measurement of the area in the bell curve ranging from +1.0 to +2.0 will have a standard deviation to be 0.8185.

 

 

When a process is 1-sigma, it is said that it is encountering more defects according to the customer specifications as compared to a six sigma operation. For a 1-sigma, there are around 690k dpmo while a mere 3.4dpmo for a 6-sigma which make it more efficient and productive to work at the latter.

 

An organization adopting 6 sigma for enhancing its process is more likely to be chosen when dealing with complex issues arising from processes. The six sigma priority for any projects in an organization should be to prioritize the project which yield the most potential customer satisfaction.

 

Given that the approach to six sigma is an entirely factual data driven methodology, it does have some limitations. The commonly used 6 sigma in reality actually refers to a 4.5 sigma level due to the introduction of a 1.5 sigma shift that is used to deal with long-run variations of a particular process. True six sigma will therefore allow a maximum of 2dpmo. For short-term calculations, true six sigma at 99.99966% is used while for long-term calculations the shifted 6 sigma is used at 99.9999998% is used.

 

In the light of the above, a management organization that entirely integrate the 6-sigma disciplinary procedures constantly measures and indefinitely enhance its process in a continuous cycle.

 

Many participants tried to answer this most basic and fundamental question. However, except for one answer all other answers were either incorrect or failed in plagiarism. There are no winners for this question. 

 

I have put a detailed explanation and the correct answer below. Kindly review.

 

Let's first look at a Bell Curve (or a Normal Distribution). In this case, Mean = 21 and standard deviation = 1.

 

 

Bell curve has a lot of useful properties, however, I am going to focus on the property that talks about the spread of data.

- If you move 1 standard deviation away from the mean on both the sides, then 68.27% of points will get covered

 

- If you move 2 standard deviation away from the mean on both the sides, then 95.45% of points will get covered

 

- If you move 3 standard deviation away from the mean on both the sides, then 99.73% of points will get covered

 

Many practitioners feel that above graph depicts a Six Sigma performance. This is probably one of the most common misconceptions in the industry. The above graph only depicts one property of a Bell Curve. Infact, we can extend this property to 4 / 5/ 6 standard deviations away from the mean on both the sides. Just for example, below is how it looks for 4 standard deviations away from mean on both the sides.

 

To visualize a Six Sigma performance, we will need to also know the specification limit. Let's fix the Upper Specification Limit at 24.

Sigma level is the number of standard deviations that can fit between the mean and the specification limit.

With the current details, this process is operating at 3 Sigma. Below is how you will visualize this process.

 

Now let's visualize a Six Sigma process. Specification Limit cannot change, hence it will remain 24. We will have to improve the process by reducing the standard deviation. Let's assume that we reduce the standard deviation from 1 to 0.5

Now 6 standard deviations can fit between mean and specification limit. Below is how you visualize Six Sigma performance.

 

Even in the improved process, the properties of normal distribution still hold good. Just for ex. - If you move 3 standard deviation away from the mean on both the sides, then 99.73% of points will get covered

 

To conclude, 

If you move 3 standard deviation away from the mean on both the sides, then 99.73% of points will get covered - this is a property of bell curve and it holds good for all normal distributions

For checking the Sigma Level, one needs to know the specification limit. And Sigma Level is the number of standard deviations between mean and specification limit. Hence not all bell curves are performing at Six Sigma Level (it depends on the position of Mean and Specification Limit).