of the readings in a series from their average value. Table 1.5 shows the number of prod-
ucts meeting requirements and the equivalent defects per million products for a range
of standard deviations.
Assuming a normal distribution of results at the six sigma level you would expect 0.002
parts per million or ppm but when expressing performance in ppm, it is common
practice to assume that the process mean can drift 1.5 sigma in either direction. The
area of a normal distribution beyond 4.5 sigma from the mean is 3.4 ppm. As control
charts will detect any process shift of this magnitude in a single sample, the 3.4 ppm
represents a very conservative upper boundary on the nonconformance rate.
Although the concept of six sigma can be applied to non-manufacturing processes you
cannot assume as was done in Table 1.4 that the nonconformities in a stage output are
rejected as unusable by the following stages. A person may pass through 10 stages in
a hospital but you cannot aggregate the errors to produce a process yield based on stage
errors. Patients don’t drop out of the process simply because they were kept waiting
longer than the specified maximum. You have to take the whole process and count the
number of serious errors per 1 million patients.
Can we keep on doing it right?
Would the answer be this? No, we can’t because the supply of resource is unpre-
dictable, the equipment is wearing out and we can’t afford to replace it.
Or would it be this? Yes, we can because we have secured a continual supply of
resources and have in place measures that will provide early warning of impending
Basic concepts 41
Sigma Product meeting Number of errors per million products
Assuming normal Assuming 1.5
distribution sigma drift (ppm)
1 68.26 317,400 697,672.15
2 95.45 45,500 308,770.21
3 99.73 2700 66,810.63
4 99.9937 63 6209.70
5 99.999943 0.57 232.67
6 99.9999998 0.002 3.4
Table 1.5 Process yield at various sigma values
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