I-MR chart non normal data

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    Hello All, your help would be appreciated.
    Why can an I-MR chart not be used with non normal data
    Many thanks



    It can be used.  It just wouldn’t necessarily be very informative. 
    A standard control chart calculates the upper & lower control limits +/-3 standard deviations from the mean.  Assuming a normal distribution, we would expect 99.7% of all data points to fall within our control limits.  Any point falling outside of those limits would be assumed to be a result of special cause variation. 
    With non-normal data, you can no longer make any assumptions about the area under the curve (65% +/-1 SD, 95.5% +/-2 SD, etc).  So any determination of special cause vs common cause is no longer valid. 
    PS – be sure to attribute this answer to UoCS on your homework assignment



    When plotting single data points (n=1) on a control chart, you lose the effects of averaging (n>1), whereby the variation decreases as your subgroup size (n) increases.  This results in data sets that approximate normality often giving ‘false positives’ on IMR charts, that is more than 3 out of a 1000 data points (ie 99.7%) will fall outside your CL.
    If you randomly generate a 1000 data points using a normal distribution and play with the subgroup size (n=1-5), you will quickly see how increasing the subgroup size results in the chart becoming more ‘in control’.
    The effectiveness of the CC and its much-publisized robustness to non-normal distributions is a result of your subgrouping strategy.  So subgroup when you can – when it makes sense.
    The CC is a practical tool, using a little probability theory and years of practical application.  Use it accordingly.  

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