Six Sigma Statistics and Answering the Right Question

Question from linkedin.com isixsigma.com group: How should Z be calculated given that there is no upper specification limit and the data are normally distributed?

Response: When helping someone in the real world and not undergoing an academic exercise, it is important to make sure we are answering the right question. For this example, I would like to ask a why questions; e.g., why do you want to calculate the Z value. It is important to know that we are not answering the wrong question to what is really needed, sometimes to the third decimal place.

Since I am responding without anybody being here, I will make some inferences. If it is planned that someone wants to calculate the Z statistic so you can calculate a sigma level for a process, I will discourage you from doing so because the sigma metric can be very confusing and misleading. I am assuming that you have also shown that your process has region of stability as demonstrated by a control chart, preferably an individuals chart tracking at the 30,000-foot-level. It is important to note that if this is the last region of stability we can also make a prediction statement about the future.

Given the above, I will assume that it is desired to calculate the Z value to eventually make a process capability statement such as Cpk and Ppk, noting that since the specification requirement is one sided, we cannot calculate a Cp and Pp value.

If this is the case, I will suggest another approach to describe how the process is doing relative to customer needs. I suggest using a probability plot then reporting the estimated percent non-conformance using the one-sided specification limit. More about this can be found about this alternative by checking out “Resolving Common Issues with Performance Indices.”

This article suggests looking and reporting how well your customer is doing relative to specifications using a system so that it is easier to understand how the process is truly doing. This methodology is one portion of the overall Integrated Enterprise Excellence system; i.e., a no-nonsense system for Corporate Performance Management (CPM).