# Non-normal capability and negative z scores

Article Revised: March 27, 2019

Here’s a question from a Pyzdek Institute Six Sigma Green Belt student:

Question: I’m currently looking at data for my Green Belt project.  The primary metric is turn-around-time, and the data is non-normal. I have run the Distribution ID plot and determined that the closest fits for my data are a Weibull distribution and a Normal Distribution with a box-cox transformation with a Lambda of 0.15. I was wondering which you believe would be better to calculate my process capability? The process is highly variable and is not currently monitored across the value stream, leading to huge variation.  A USL of 100 days has been determined through VOC, using this I get the following Z.Bench: -0.16 using the box-cox transformation and -0.18 using the Weibull. Could you please advise what is the best course of action for determining the sigma level of this process (fully expected that it is low due to the nature of how the process is administered)?

Answer: Any time you have a negative Z score, things are pretty bad. I presume that the error rate is very extreme. Many Six Sigma experts suggest that you not bother with Z scores or sigma levels for extremely poor processes. I’m okay with just knowing the historical error rate in this case and not asking for the Z score or historical sigma level.

As far as whether the Weibull or Box-Cox is the better choice, it really doesn’t matter, although you might want to know the p-value for the fitted curve for each (I.e., is the lack of fit significant?) Both methods are examples of what is called “curve fitting.” Both are just trying to find equations for curves that do a decent job of describing the distribution of the data. In scientific and engineering work equations are based on known understanding of how nature works, which is superior to mere curve fitting. In business we usually must rely on curve fitting to describe our processes and our data, but there’s no real reason to prefer one curve fitting method over another as long as they both do a good job of fitting the data.

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