Feb 142012

During a PMP class discussing PMBoK’s Quality Management knowledge area, a couple of participants, after finding out the allowable defects in six sigma quality, were of the opinion that this level of expectation of quality is unrealistic and too high. 3.4 defects per million does seem hard to achieve but after sharing with them the number of errors under 3, 4 and 5 sigma and explaining with an example, it was clear that hitting six sigma my be the right choice in some areas but not all.

Example 1:(Cost of rework very low)

Let us assume a plant produces bolts at a rate of 10 million per month and is expected to last 10 years. The cost of each bolt is $1. A defective bolt is discarded since fixing cost is too high. So waste for each sigma level is as follows:

6-Sigma: 3.4 def/mil > 34/10mil > $34 waste/month > $408/yr

5-Sigma: 233 def/mil > 466/10mil > $466 waste/month > $5,592/yr

4-Sigma: 6,210 def/mil > 12,420/10mil > $12,420 waste/month > $149,040/yr

3-Sigma: 66,807 def/mil > 133,614/10mil > $133,614 waste/month > $1,603,368/yr

Improving one sigma level requires $1 million initial investment plus maintenance cost of $50,000/year.

From 3-Sigma to 4-Sigma, total cost is $1.5 million and savings are ~$14 million (Difference between 3-Sigma and 4-Sigma over 10 years).

From 4-Sigma to 5-Sigma, total cost is $1.5 million and savings are ~$1.5 million (Difference between 4-Sigma and 5-Sigma over 10 years).

From 5-Sigma to 6-Sigma, total cost is $1.5 million and savings are ~$50,000 (Difference between 5-Sigma and 6-Sigma over 10 years).

So Benefit/Cost Ratio is very high to move from 3-to-4 sigma, and comes as 1 for 4-to-5 sigma but is below 1 for 5-to-6 sigma. So moving to 5 sigma makes business sense but moving to six sigma is not cost effective. The cost of Quality is too high and benefit does not justify the cost.

Example 2:(Cost of failure very high)

Now let us look at another example where cost of failure is very high. Assume that a plant produces dust masks at a rate of 1 million per month.

25% are used in highly hazardous areas where failure will likely result in death,
25% are used in areas where serious health issues are likely requiring lifelong care,
25% used in moderately risk areas with temporary care, and
25% in low risk areas with minor inconvenience and medication.

The costs associated with each failure is $1,000,000 for death related, $2,000,000 for permanent care, $20,000 for temporary care, and $200 for inconvenience. We also assume that 50% of failures are qualified as manufacturers fault and thus is liable for damages given above.

Total cost of failure for various sigma levels is:

6-Sigma: 3.4 def/mil > ~1 def/2.5mil > $1mil+$2mil+$20k+$200 = ~$3 million (minor cost of failure)

5-Sigma: 233 def/mil > ~60def/2.5mil > $3mil(cost of 1def) x 60 = ~$120 million (may not survive for long or profit erodes)

4-Sigma: 6,210 def/mil > ~1050def/2.5mil > $3mil x 1050 = ~3 billion (cannot operate with such cost of failure)

3-Sigma: 66,807 def/mil > ~17,000def/2.5mil > $3mil x 17,000 = ~51 billion (cannot operate with such high cost of failure)


From 3-to-4 Sigma, cost is $20mil and savings are $24 billion

From 4-to-5 Sigma, cost is $40mil and savings are $1.4 billion

From 5-to-6 Sigma, cost is $50mil and savings are $58 million

It makes perfect sense to reach a quality of six sigma in this case as the savings still are higher than cost.



Improving quality to six sigma level may be justified when the cost of failure is very high but may not be cost effective when failure cost is very low. Of course, it depends on investment for improvement of sigma levels and cost per failure.

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