Non-Normal Process Capability

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    I want to study the process capability of Complaints resolving cycle time.

    I collected the cycle time data for one month. The data has the following statistics:
    P-value < 0.005
    Skewness: 1.01864
    N: 1850

    I want to identify the data distribution using Minitab to be able to study the process capability based on the identified distribution p-value for all distributions was < 0.05 so the collected data does not follow any of distributions what can in this case.

    Can you help, please?


    Robert Butler

    Please understand I’m not trying to be snarky, condescending, or mean spirited but your post gives the impression that all you have done is dump some data in a machine, hit run, and dumped out a couple of statistics that suggest your data might not exactly fit a normal curve. To your credit it would appear you do know that one of the requirements for a basic process capability study is data that is approximately normal.

    Let’s back up and start again.

    I don’t have Minitab but I do know it has the capability to generate histograms of data and superimpose idealized plots of various distributions on the data histogram.

    Rule number 1: Plot your data and really look at it. One of the worst things you can do is run a bunch of normality tests (or any kind of test for that matter) and not take the time to visually examine your data. One of the many things plotting does is put all of the generated statistics in perspective. If you don’t plot your data you have no way of knowing if the tests you are running are actually telling you anything – they can be easily fooled by as little as one influential data point.

    So, having plotted your data:

    Question 1: What does it look like?
    Question 2: Which ideal overlaid distribution looks to be the closest approximation to what you have?

    Since you are looking at cycle time you know you cannot have values less than zero. My guess is you will probably have some kind of asymmetric distribution with a right hand tail. If you wish you can waste a lot of time trying to come up with an exact name for whatever your distribution is but given your kind of data it is probably safe to say it is approximately log normal and for what you are interested in doing that really is all you have to worry about.

    One caution: if your histogram has a right tail which appears to have “lumps” in it – in other words it is not a “reasonably” smooth tapering tail you will want to go back to your data and identify the data associated with those “lumps”. The reason being that kind of a pattern usually indicates you have multiple modes which means there are things going on in your process which you need to check before doing anything else.

    If we assume all is well with the distribution and visually it really is non-normal then the next thing to do is choose the selection in Minitab which computes process capability for non-normal data. I don’t know the exact string of commands but I do know they exist. I would suggest running a Google search and/or going over to the Minitab website and searching for something like capability calculations for non-normal data.

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