Forum:When I see data that follow a normal distribution, I am, at first, suspicious. I saw this only once for the daily output of a nuclear fuel processing facility. It was unusual enough that the Quality leader had me fly me out to the site to investigate. The data was gathered in a manner that obscured the problem and was a consequence of the Central Limit Theorem (CLT).On another project, when I demonstrated the deviations from the usual, though non-normal, distributions of cycle time for engineering cycle time, the same Quality Leader told me that I had finally demonstrated the differences in a process that many MBBs had failed to do so. We proved that restructuring the business segment (over $1BB/year in revenue) was the best thing to do. The person responsible for the restructuring was later promoted to CEO of a large business unit of GE.Another application of understanding deviations from the usual, but non-normal, probalility distributions was identifying the process drivers during a major fraud/bad debt project involving on-line transaction processing. Once the parameters of the non-normal distributions were determined, deviations could be flagged, ranked and investigated. The processes are routinely monitored using control charts with tranformed data to flag fraudulent transactions in real time.This philosophy of identifying deviations from well understood, but non-normal, probability distributions is not uncommon in fraud, risk and credit scoring applications and is key to understanding what the data is telling you about the process. You learn more about the process from the “outliers” than anything else.In general?Always have a look at your raw data using a run chart. You should be able to see if there are significant events (potential Vital Xs) that make a difference to your process. The naysayers will tell you that these are unusual events and, therefore, unlikely to reoccur so you should ignore the data. Ignore this advice, but note that they have unconciously given you a potential Vital X).This information will allow you to show the behaviour of the process when it is under only common cause variation and when there is an event that results in the process behaving “out of control.” Examples include special orders, end of month or end of quarter effects, expedited orders, unusual requests, etc.It is quite likely that the process is non-normal because you are looking at the superposition of two processes; the normal process and the “special case” process – each will have its own characteristics, and the result will look very irregular. Have a look for bimodal distributions – this is a BIG clue that you have two processes.When you are trying to characterize the DPMO for your baseline performance as part of Measure, use a discrete measurement (over or under specification). It is likely that your DPMO is VERY high. The mechanics of whether you have discrete or continuous data is unimportant if your baseline DPMO is 900,000 during the Measure phase.Once you have completed your project, you may have two streams for repeat customers and new customers, for example. NOW you may find that each subgroup is normally distributed (or other well-known distribution, exponential or Weibull) and can use continuous data with the same USL and LSL you used to classify your baseline data into error/nonerror in your Measure phase. You may either transform your data using a Box-Cox transformation or Johnson transformation to do the calculation. MINITAB allows you to directly calculate the process capability assuming a particular distribution wihtout having to transform the data to begin with.Cheers, BTDTP.S. – I haven’t read it, but Andy Sleeper has a new book on probability distributions in Six Sigma projects called “Six Sigma Distribution Modeling,” McGraw-Hill 2007.P.P.S – I am not Andy Sleeper.P.P.P.S – He is not paying me either ;)
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