Non-Normal Data on Control Charts – Transformation vs Percentile Methods

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    If a Non-Normal data has to be plotted on a XmR Chart, then it has to be transformed to Normal Data and then it shold be plotted, because XmR Chart is very sensitive to Non-Normal data. If a data could not be transformed from Non-Normal to Normal, is it advisable to use Percentile Techniques in the place of UCL, CL and LCL.
    0.9987 th Percentile is used as UCL
    0.50 th Percentile is used as Centre Line
    0.0.00135th Percentile is used as LCL.

    I have seen some use the above techniques, and some use non-normal data directly on XmR chart. In this connection, I would want to know your comments.



    I have been having much the same problem regarding non parametric data that cannot be transformed to a normal distribution. The use of the 0.135th percentile and 99.865th percentile to define the spread of the data and 50th percentile (i.e. the median) to define the location of the process is fine when performing a Weibull capability study but is not suitable for he production of a percentile control chart. This is because by definition it will always give rise to a control chart with out of contol points.

    This poses a proble because you are supposed to check that the process is in control before attempting to perform a capability study on the process.

    At Motorola we use a JMP templat called PERCEST which was decribed as generating Estimated Control Limits and Center Line for use with an Indiviuals Control Chart.

    These limits, I believe, are wider than those used to define the data spread for the Capability Study. Unfortunately I nolonger have the file. Nor do I have access to the calculations used in it. Does anyone know how to calculate these limits or have a copy of the JMP template?



    It is my understanding that control charting – especially XbarR charts – are largely robust to non-normally distributed data. I would advise you use the tool as intended, as a practical method of assessing your process relative to it’s predictability. I wouldn’t over think this one. Reference Wheeler or Demming for additional insights. Good luck.

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