Question

It has been estimated that a company operate at about the 6? level. Show that 6? quality level implies 3.4 ppm

Answer 1

It has been studied by the researchers that in the long run any process and its output will not remain the same as it was desired and thus will experience a change because variation is the law of the nature and is inevitable (statistically the change is 3 times the standard deviation of that process i.e. 1.5 times of standard deviation from mean in any of the direction - upper or lower). Then those researchers tried to estimate the boundary/limit/specification of the variation or the change so that if the process is controlled within that limit then what is the probability of occurrence of failure. That limit was calculated through probability distribution and it came out to be as 4.5 times the standard deviation because beyond the 4.5 sigma, the probability of occurrence is 0.000017 from the mean (based on probability distribution).

Therefore, from both the sides of the mean, the occurrence of variation is 0.000017 x 2 = 0.000034, which is 3.4 in 1 million.

Now this 4.5 sigma is the shift beyond the natural variation of 1.5 sigma, thus it has been inferred that if a process limit is maintained at 6 sigma on each side of the mean, then probability of occurrence of defect is 3.4 in 1 million.