six sigma & levels of sigma processes

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Six Sigma

Accurate and Precision Six Sigma can be best

explained by using the analogy of a rifle firing at a target.

Six Sigma in simple terms

Accuracy and precision With the center of the target taken to be

the true value of the characteristic being measured and by the rifle shots representing the measured values, there are four combinations of accuracy and precision as depicted in the following slides.

Inaccurate and imprecise

Accurate and imprecise

Precise but inaccurate

Accurate and precise

Objectives of Six Sigma

As observed from the Picturization in the preceding slides, the objective of moving towards world class manufacturing a is to continuously achieve greater consistency of the processes by aiming for higher levels of accuracy & precision

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Sigma in statistical terms

Standard deviation is also referred to as the Greek letter sigma in quality management literature. Consequently process variation can be described by how many sigmas ( i.e how many multiples of standard deviation or SD ) fit within the specification limits.The higher this number, the better is the quality and vice versa.

Sigma is a statistical measure of the quality consistency for a particular process / product.

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Sigma process

From a sigma process we come to know that at what distance, in terms of the standard deviation, the specification limits are placed from the target value.

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Move beyond 3 sigma

Until a few years back all statistical process controls were designed on the basis of 3 sigma limits. It is only in the recent years that this concept has been challenged and the organizations have started looking for quality levels beyond 3 Sigma.

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3 Sigma process

LSL USLMean=8SD = 2

- 3 SD + 3 SD

2 3 4 5 6 7 8 9 1210 16151413111

Note : LSL is Lower specification limit and USL is Upper specification limit.

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4 Sigma process

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LSL USLMean=8SD = 1.33

- 4 SD + 4 SD

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LSL USL

Mean=8SD = 1.07

- 5 SD + 5 SD

5 Sigma process

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LSL USLMean=8SD = 1

- 6 SD + 6 SD

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6 Sigma process

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Precision

Lesser the standard deviation of the process, more precise or consistent is the process

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3 Sigma Vs 6 Sigma

The goal of Six Sigma program is to reduce the variation in every process to such an extent that the spread of 12 sigmas i.e. 6 Sigmas on either side of the mean fits within the process specifications. The figure on next slide shows what this looks like.

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LSL USL

6 Sigma curve

3 Sigma curve

3 Sigma Vs 6 Sigma

In a 3 sigma process the values are widely spread along the center line, showing the higher variation of the process. Whereas in a 6 Sigma

process, the values are closer to the center line showing less variation in the process.

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3 Sigma Vs 6 Sigma

The comparison on the previous slide also shows a process in which the process spread of Six Sigmas (ie. 3 Sigmas on either side just fits within the specifications). In this case one must be extremely careful to ensure that the process average never slips off the target, otherwise the curve will shift and non-conforming items will increase. With Six Sigma requirement the process mean can shift by as much as 1.5 sigma before the likelihood of non-conforming items is increased. Even if the process mean does shift off center by as much as 1.5 sigma, only 3.4 non-conforming items per million parts should result.

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Amount of process shift allowed

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LSL USL

SD = 1

1.5 SD 1.5 SD

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Sigma levels and defect rate

Quality level % Quality Defective PPM*

3 Sigma 99.73 66807

4 Sigma 99.9937 6210

5 Sigma 99.999943 233

6 Sigma 99.9999998 3.4

*Parts Per Million

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Sigma levels & Cost of quality

Sigma Defect rate(PPM) Cost of quality Competitive level

3.4 <10%

233 10-15%

6210 15-20%

66807 20-30%

308537 30-40%

6,90000 >40%

World Class

Industry Average

NonCompetitive

6

5

4

3

2

1

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