Prediction Statement for a Non-Normal Data Response

In Lean Six Sigma Black Belt training often students are not sure what to do with non-normal data. This should not be a concern, as illustrated in the follow example.

Question: The response of interest is the number of elapsed days from a vessel discharge to container release from a port for customer delivery. Since the data has a natural level limit of zero, the data are not normally distributed. The desire is to be able to predict the probability of container being dispatched for any time; e.g., 80% of all containers are dispatched in 8 days or less.

Response: Before prediction statements are made it is important to first determine if our process has demonstrated stability. If this is not done, our answer could be very deceiving. To illustrate this point, consider something changed three months ago in our process. If all data were lumped together for an analysis, the answer would not predict the process in the future as it is known today. We really should have used only the data since the process shift to make the prediction statement.

A technique for assessing predictability is 30,000-foot-level control charting. When this methodology is used we need to have an infrequent subgrouping so that the variability that typically occurs between subgroups appears as common cause variability. There might be expected to be differences by day of the week shipped. If this were the cause, we could pick a minimum subgrouping of weekly. If there is expected to be a difference by week of the month, then one should not subgroup any less frequent than monthly.

You will need to delay time-series reporting since it takes some time for shipments to arrive. This delay in data reporting should be a time large enough so that a majority of shipments are expected to arrive. If you don’t do this you would need to deal with censored data.

An x-bar and s chart is not appropriate since variability between subgroups needs to be considered as a possible common cause source, an individuals control chart needs to be used to assess stability.

When assessing stability/predictability the mean and standard deviation (log standard deviation plot might be better since standard deviation is not normally distributed by its nature) on individuals control charts. There would be one chart for mean and there would be another chart for standard deviation. The charts would have a weekly or monthly subgrouping.

One observation of the control chart might uncover seasonality difference. The holiday delivery season shipments might be indicated to take longer. A prediction statement for regions of stability can be made. It might be appropriate to make a prediction statement for holiday shipment season; i.e., separated from the rest of the year.

For stability regions, the original data from this region can be plotted on a probability plot. A log-normal probability could provide a good fit. Since there is so much data, one might just plot a random sample of the data. The percentages of interest can be determined from the probability plot for stability regions. If all data are used confidence intervals will obviously be very tight.

An example data-transforming situation is described in “NOT Transforming the Data Can Be Fatal to Your Analysis: A case study, with real data, describes the need for data transformation.”

The types of measurements described for situations like this is used as performance measures in an Integrated Enterprise Excellence (IEE) business system, which goes beyond Lean Six Sigma and the balanced Scorecard.

The following link provides more IEE information: “The Integrated Enterprise Excellence System: Benefits and Implementation.” Provided in this link is access to many articles, webinars, books, 1-day seminar, etc. The 4 book-volume series described in the above link can be purchased in many places, including Amazon.com. The E-DMAIC sequence of book topics is covered in Volume 2. The P-DMAIC sequence of book topics is covered in Volume 3.

Link: The Integrated Enterprise Excellence System for Corporate Performance Management