Sigma score and nonnormal data
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 This topic has 9 replies, 4 voices, and was last updated 12 years, 1 month ago by Mikel.

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October 30, 2009 at 8:45 am #52858
When calculating a sigma score for nonnormal continuous data I was taught that you should convert to discrete data as the continous calculations will only work with normal data.
I have recently been told by an “MBB” that this doesn’t matter and you should treat as continous anyway as it doesn’t matter. This doesn’t ring true to me.
Which is correct?0October 30, 2009 at 11:53 am #186484The whole concept of calculating sigma score is flawed as we have established quite well on this Forum. The bottom line is that we are trying to establish the capability of a process. If the data is continuous, you can do process capability for any type of data, normal or not. If it is discrete you can also calculate a process capability. Minitab handles both situations well. Usually when you shift from continuous to discrete for sigma calculations you are going from some continuous value to a defective count. Even then there is some assumption of the normal approximation to the binomial (defective/not defective). In all cases, the calculations don’t provide much and when you add the dreaded 1.5 shift it is just an exercise.
0October 30, 2009 at 12:18 pm #186486I agree with this being an excercise but I thought that in calculating the score it used calculations based around standard deviation of the data and how they fit into the customer requirements.
If your data is nonnormal isn’t this worthless as the standard devitation does not indicate the shape of the data in anyway.0October 30, 2009 at 1:31 pm #186488Hey Doc,
So what do you reccomend in terms of baselining the capability of a given process? I have followed the threads as to the weakness of sigma, but don’t recall the solution (if one was ever provided)….What are your reccomendations for a metric? Thanks!!0October 30, 2009 at 1:53 pm #186490There are a couple of ways to calculate sigma level. One is the tried and true DPMO which you see very often in some sort of table. It usually includes the shift. In that case you are using defectives as the basis. Then some normal assumption to the binomial is used and a “Z value” is calculated. Then the shift is put in. The binomial is pretty robust to the normality issue. If you are truly using continuous data then you again are calculating a z value and looking up in the z table. The shift is usually added on top of that.All distributions, normal or not, have a measure of dispersion. That is, all distributions have a defined s.d. although it is calculated differently than the normal distribution. That is why you can do process capability for any distribution.
0October 30, 2009 at 1:55 pm #186491Cpk has been around a lot and can be calculated for any distribution. Sigma level is OK, that is the DPMO calculation but don’t use the 1.5 shift. It is worthwhile to calculate the true long term shift if there is one.
0October 30, 2009 at 2:43 pm #186492Thanks Doc!!
0October 30, 2009 at 3:33 pm #186493If there is one?Ever seen a process that is absolutely steady?
0October 30, 2009 at 3:37 pm #186494Steady is a relative concept. We could say “in control”. I just can’t get into the concept of worrying about and distinguishing short term and long term. Too much energy for too little return of information.
0October 30, 2009 at 4:39 pm #186495Agreed. Just have to have margins on true short term data, like
equipment qualification.0 
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