In some instances the tail beyond the nearest spec limit has virtually all of the defects. For instance, suppose the mean happens to lie 2 standard deviations from the upper spec limit, and 4 standard deviations from the lower limit. This means there is about a 2.3% likelihood of a defect beyond the upper limit, but only a 0.003% likelihood of a defect below the lower limit – a factor of 70,000 times as many defects in the upper tail.
In other instances, both tails might be important. If Z(Upper tail) is 2, and Z(lower tail) is 2.2, then you have to account for both sides of the distribution.
Most software packages do this by adding both tails’ probabilities together, and computing an “equivalent” Z value that corresponds to that total number of defects.
I have a simple Excel template that handles this. You enter the process mean and standard deviation, along with one or two specification limits, and it computes the Z value. If you send me your email I will send it along. If the “isixsigma powers that be” want to make it available for all, I will be happy to share.
Bear in mind: if the data are discrete, or if continuous data are non-normal, this template is the wrong one to use. I also have a template for discrete data.
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