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X-Bar R Charts

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  • #50408

    Almudena
    Participant

    I have a destructive testing on the line and we took 3 piece sample,  plot the average and range in an X-Bar R Chart to monitor weld-strength. The individual readings do not follow a normal distribution.
    The process is in-control, based on this fact we compute the Cpk however one of our managers challenge its validity because the distribution of the individual readings is not normal…
    Our response was that that was the purpose of the central limit theorem, and that based upon the central limit theorem we could use the averages and ranges from the control chart to estimate the Cpk value.
    What is wrong with the inference?
    I would appreciate any comments and/or references.
    Thanks
    Almudena

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    #173288

    Michael Mead
    Participant

    Hi.
    I see several things wrong. First, you say that the process is in control because you compute the CpK…the two concepts of capability and control can’t be tied together through the capability index. Control indicates a stable process, while capability indicates that the specification can be met to some degree.
    Second, the central limit theorem states that averages will be approximately normally idstributed regardless of the distribution of the individual observations. I don’t see how that relates to your problem at all.
    Your manager is correct. CpK has an underlying assumprtion of normaility. My guess is that your data is skewed right. Since you are probably dealing with a single-sided specification, you should calculate the CpL (lower side of CpK) based on the individuals, not the average and range.
    I am sure other people will elaborate more on this.

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    #173295

    Ron
    Member

    Normality IS NOT A REQUIREMENT when using Shewhart control Charts…This thought trail was misapplied in GE and somehow escaped into the general community.
     
    Please help putting a stop to this falsehood.
     
    Thanks

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    #173301

    Michael Mead
    Participant

    Ron, how does this comment (which is correct) apply to the question? Control charts work for any shape distribution, but the CpK is based on a normal distribution. Some software packages calculate it somehow. I have no idea what they use. 

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    #173303

    Savage
    Participant

    I generally agree with Michael.
    One note is that you will never, I mean never, have a distribution that is perfectly normally distributed. The idea is that if your distribution somewhat resembles the bell curve, calculate things like Cpk in the usual fashion. So, if your distribution is significantly different from the normal, you might tell the software you are using to “Assume distribution is not normally distributed.”

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    #173306

    Ron
    Member

    There is no correlation between constructing a control chart (Xbar &R) and Cpk. These are two very different concepts.
    Cpk refers to the centering of a process around specification limits. Control Charts refer to Statistical Control Limits and represent the voice of the process.
    Central limit theorem does not come into the discussion when referring to control charts. It does come into the discussion of Nortmailty which as previously stated is out of scope for control charts but germane to process capability.
     
    So to answer your question since you asked two of them.
    Normailty not required for control charts
    Is required for process Cp calculations to be valid.

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    #173334

    Almudena
    Participant

    Thank you Michael and Ron for your help, now I have a better undestanding of these concepts.
    Regards,
    Almudena

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