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Normality test for x bar charts

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Viewing 17 posts - 1 through 17 (of 17 total)
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  • #49158

    MM
    Participant

    Hi – are we required to check notmality of data before doing x bar control chart? I know that for IMR we are supposed to do so. Help pls.

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    #167551

    Ron
    Member

    c
    shewhart control charts are robust and do NOT require a noraml data set.

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    #167553

    MM
    Participant

    hmmm…I am currently in a trng and the instructor is saying that we require to check that…guess will have to read more about this…thanks.

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    #167554

    Ron
    Member

    Best check the instructors credentials.
     
    See Wheeler Understanding Statistcal Process Control

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    #167562

    Old MBB
    Participant

    Normality is not a requirement to use a Control Chart, but it may have a direct impact…  If you have, for example, a lognormal distribution that is highly skewed, you may encounter failures in your I-chart due to an unusual number of points occuring beneath the mean line.  Bi-modal distributions may fail due to too many points greater than 2s from the mean, etc.  Non-normal doesn’t mean you can’t use control charts, it just may mean you’ll have to modify which of the ‘tests’ are appropriate…

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    #167852

    Anonymous
    Participant

    This comes down to who you follow: Wheeler or Montgomery et al.?
    Personally I an convinced that Wheeler is wrong on the robustness of Individuals with extreme Skewness and/or Kurtosis. Numerous published simulation studies (aside from Wheeler’s books) clearly show that Type 1 & II error rates become unacceptable. 
    Therefore a Box-Cox, Johnson transformation or distribution fit is appropriate and necessary.  If you transform and want to plot the raw data, simply apply the inverse transformation to get the control limits.  This is straightforward with software tools.
    Of course this debate has gone on for years and will not be resolved here. You are wrong to state that any instructor who does not follow Wheeler is incompetent.  I have read all (yes all) of Wheeler’s books but that doesn’t mean that I have to be his disciple.

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    #167856

    DaveS
    Participant

    AnonymousYou stated,
    “Numerous published simulation studies (aside from Wheeler’s books) clearly show that Type 1 & II error rates become unacceptable.”
    Can you provide a reference or two. I want to read these studies, but a Google search doesn’t disclose any.
     
    Thanks

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    #167861

    Anonymous
    Participant

    Please note that I am not questioning the robustness of the x-bar chart. We are talking about the lack of robustness to non-normality for Individuals charts.
    Some references supplied below. Before you go to the library, do the following:
    1.     Simulate 100 observations from an Exponential Distribution with scale=1 and threshold = 0.
    2.     Create an IMR chart with all tests for special causes. Count the number of alarms (these are all type I error).
    3.     Run a Box-Cox Transformation on the simulated data (save the transformed data)
    4.     Repeat Step 2.
    SPC References:
    Spedding TA and Rawlings PL, “Non-normality in Statistical Process Control Measurements” International Journal of Quality and Reliability Management, Vol 11 No 6, 1994, pp 27-37.
    Montgomery DC, Introduction to Statistical Quality Control – 5th Ed.,  pp237-238.
    Borror CM, Montgomery DC, Runger GC, “Robustness of the EWMA Control Chart to Non-normality”, Journal of Quality Technology, Vol 31, No 3, 1999.  (Shewhart Charts are included in the simulation study)
    Process Capability References:
    Somerville SE and Montgomery DC, “Process Capability Indices and Non-Normal Distributions, Quality Engineering, 9(2), 305-316.
    Tang LC and Than SE, “Computing Process Capability Indices for Non-Normal Data: A Review and Comparative Study” Quality and Reliability Engineering International, 15: 339-353.
    English JR and Taylor GD, “Process Capability Analysis – A Robustness Study” International Journal or Production Research, 1993, Vol 31, No 7, 1621 – 1635. 
     

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    #167862

    Ron
    Member

    Repeat !!!
     
    Normality is not a requirement for Shewhart Control Charts.
     
     

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    #167867

    Anonymous
    Participant

    Repeat after me.
    I will obey the teachings of Dr. Wheeler for He is Omniscient.
    I will obey the teachings of Dr. Wheeler for He is Omniscient.
    I will obey the teachings of Dr. Wheeler for He is Omniscient.

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    #167893

    JC
    Participant

    No.  It is what it is.

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    #167904

    Anonmousalso
    Participant

    You must be a GE BB  they all hang on normality. Even when it doesn;t matter.
     

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    #167908

    Anonymous
    Participant

    Not GE, but 20 years in SS.
    I don’t care when normality doesn’t matter. I care when non-normality matters and costs real money because you’re chasing after false alarms and failing to detect genuine assignable causes.
     

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    #167917

    Jonathon Andell
    Participant

    I would look at the raw data on a control chart, to see if the process appears stable. Process instability can make data normally distributed data look non-normal.
    It also is OK to check for normality, once you know whether your process is stable. It’s OK to use Anderson-Darling and Box-Cox, but also remember to generate probability plots – a graph is worth a thousand hypotheses.
    If the data truly are non-normal, you need to align your decision with the current use for the data. If it’s a look back to establish process capability, you simply want an appropriate model to make a sound estimate. If you are moving forward to control the process, you need to determine how big a penalty you pay for a decision error. If the penalties are moderate, and if your control limits lie well within spec limits, the hassle of a transform may not be warranted.
    Whatever else you do, watch out for one-size-fits-all answers, whether they come from the Wheeler or the Montgomery camps.

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    #167918

    Anonymous
    Participant

    Good post Jonathon.  Are you going to ASQ’s LSS Conference?  I’ll e-mail you directly so you know who I am.

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    #167920

    Jonathon Andell
    Participant

    I’ll be there (I live in greater PHX). My email is [email protected].

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    #167976

    6Sigma Below The Belt
    Participant

    I personally think that there is no need to check for normality first before doing xbar chart because there are some metrics such as turnaround time which will naturally skew and be not normal but still can be plotted in xbar chart.

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