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Help with Capability Issue

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  • #43860

    PH
    Participant

    Hi,
    I have taken 80 measurements with the following results.
    Mean = 1.97375
    SD = 0.4046
    P = 0.023
    I am after CL of (UCL 2.75 and LCL 1.25).  Even though all of the samples I measured are within this CL’s I only get a Cp of 0.42.  I’m not sure what this is telling me about my capability.
    Please help

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    #139704

    sixsigmadeewana
    Member

    what formula are you using for Cp?

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    #139705

    Adrian P. Smith
    Participant

    Hi PH,
    Are you sure you are not confusing CONTROL limits with SPECIFICATION limits?
    Cp is calculated from specification limits (i.e. the tolerance limits usually defined by the customer). Cp = (USL – LSL)/(6 x sigma)
    Control limits (LCL/UCL) are usually calculated as part of a control chart to determine whether the process is in statistical control or not and have nothing to do with process capability.
    Bear in mind also that the calculation of both Cp and your control limits require that your data be normally distributed.

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    #139712

    PH
    Participant

    I am just performing a graphical summary in Minitab.

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    #139713

    sixsigmadeewana
    Member

    means you have a lot of variation in the process and possibly a bi modal distribution. can you uplolad the data file on this forum?

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    #139715

    PH
    Participant

    Yes,
    Sorry I meant USL and LSL.  My mistake
     
     

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    #139716

    PH
    Participant

    Here are the 80 measurements.
    2.61.52.71.32.71.62.71.32.51.42.01.82.71.42.51.52.41.62.51.52.21.82.21.62.31.42.01.92.61.42.41.62.61.42.51.62.61.32.31.62.11.92.21.72.31.72.61.42.11.61.81.92.11.52.11.82.11.82.21.72.11.92.21.72.41.72.51.62.11.92.31.72.02.02.21.71.91.92.11.9

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    #139717

    Szentannai
    Member

    Hi PH,
    there is a nice pattern in this data, one high value is followed by a low value which is followed by a high value.
    I’d say that you need to clarify this first : why is this happening, is there a time dependence or is it a mixture of two populations, etc. before you start with the process capability.
     
    P.S. I wonder if I’ll be the first to point this out ? I bet there will be a bunch of similar mails.

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    #139718

    Brit
    Participant

    What is your target value – what are you shooting for?

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    #139719

    Brit
    Participant

    This process goes up and down like a yo yo.  There is a definite pattern when you plot the data.  My advice – before wondering about capability, determine the reason for the cyclical pattern.  This abnormal pattern will affect any capability analysis and solving it will help you ge the proper measurement of hitting your specs.
    Your capability index that you calculated will probably not be right if you did not fit the distribution (using minitab, JMP, etc.). My guess is this is not a normal distribution – probably bimodal or poisson.

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    #139720

    Szentannai
    Member

    Hi,
    looking a bit more at the data, could it be that you took the measurements during the startup of the process? It sure looks  like some kind of transient to me.
    Regards
    Sandor

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    #139721

    sixsigmadeewana
    Member

    This is not a normal distribution. p value is 0.023.
    As Sandor pointed out, there is a mixture of 2 or more populations here. I also think, you need to take a look at the measurement system. Is it adequate? Is it working correctly? Or even, Are the operators making up these numbers?
    The limits that you specified in the first post, are they the specification limits or control limits?
     

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    #139723

    Adrian P. Smith
    Participant

    Hi PH
    As others have said, there is a “problem” with oscillation in this data, however you never said that the data was actually time-ordered.
    A more fundamental problem is that you have spec limits expressed to 2 decimal places and data accurate to only 1 decimal place.
    It also strikes me as very odd that your minimum measure is 1.3 (your LSL rounded to 1dp) and your maximum measure is 2.8 (your USL rounded to 1dp). With 80 measures in your sample this strikes me as more than coincidental.
    Is your process actually capable of producing a measurement outside these spec limits?
    Is whoever is taking the measures perhaps rejecting out-of-spec parts without your knowledge?
    Have you already performed a Gage R&R on  your measurement system?
    Personally I think your data are suspect and I would fix that before worrying about capability or any other apparent issue (e.g. the oscillation).
    Perhaps if you posted a bit more background about your process and measurement system?

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    #139724

    Adrian P. Smith
    Participant

    OK, before I get flamed the maximum value is 2.7 not 2.8, but my point still stands. :)

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    #139726

    sixsigmadeewana
    Member

    I agree Adrian…this data somehow seems to be “made up” …. or the measurement system needs refinement. But to answer your original question, the Cp that you calculated was correct but the distribution is not normal, so you cannot really use Normal dist.

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    #139727

    Robert Butler
    Participant

    I’ve been trying to respond to this thread but the machine keeps kicking me off.  I reported the problem so this is a test to see if it has been corrected.

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    #139728

    Robert Butler
    Participant

    Ok, looks like we’re back in business.
      1. If we assume the data is time ordered then the pattern that emerges is interesting in that the process seems to be converging to a target of around 2. 
       2. Even if the data isn’t time ordered the distribution is definitely truncated.  The truncation makes the data non-normal, however, the truncation also answers the questions raised in the initial post – all of the data for this “sample” is indeed between the limits however, the capability calculation is assuming a normal distribution.  If this is a truncated normal then the actual process will make a lot of product outside the limits.  This high probability of out of spec material is reflected in the initial capability calculations.
      I agree with the other posters – the odd nature of the data suggests you need to do a lot more investigation before you try to do a capability calculation.

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    #139734

    PH
    Participant

    Hi,I was only gone for a moment and seemed to have generated quite a response.  Let me add a little context.  Thinking about it these measurements are oscilating for a simple reason.  It is the measure of a label within a piece of carried material i.e. the distance from the edge of the label to the edge of the rectangle of carried material.  Each pair of measurements are from opposite edges of a single label.  As there is little variation in the size of the carrier each pair or measurements will probably total approx 4mm.  The ideal (target) position of each label is a 2mm distance from the label edge to the edge of the carrier.
    I have already completed R&R and it was good and I took all the measurements myself.
    PH
      

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    #139735

    sixsigmadeewana
    Member

    you took all the measurements yourself ?????? That woudnt be a R&R then…It would be more like capability study…

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    #139736

    PH
    Participant

    I took the measurements in this sample myself not for the R&R.  That would not be an R&R now would it.  Give me a little credit.  3 operators carried out the R&R on 10 samples with my instruction and supervision.
     

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    #139737

    sixsigmadeewana
    Member

    just checking !!!!

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    #139738

    Brit
    Participant

    I know you’ve been bombarded.  Basically, in my opinion, the answer to your question:
    Why am I getting a cp value so low when all my stuff occurs between the spec limits?
    It’s because the data is not normal.

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    #139744

    BTDT
    Participant

    PH:

    PH: This is fascinating problem. You can get your process to Cp
    ~ 1.25 – 1.36 without much effort. You have a clear drift of the position of a
    labels that is masked by the way the data was collected.. 1)     
    Your data has some negative kurtosis. The tails of the
    distribution are fatter then you would expect for a normal distribution. This
    will result in a standard deviation that is larger than it would be for a
    normal distribution with about the similar range.2)     
    This may be due to a natural limit on the low side of 1.3 and
    on the high side at 2.7. The tails are a bit chopped off.3)     
    The entire set of data has a great deal of autocorrelation.
    Calculate the partial autocorrelation in Minitab to see that the Pearson’s
    correlation is –0.846 (p-value 0.000).
    This shows up in the run chart as the oscillation. This is a natural
    consequence of taking measurements on both sides of the same label.4)     
    There is ‘some’ problem with the resolution of the gauge, but
    it is not a serious one. The problems would only get a bit more clear with an
    extra decimal place.5)     
    Label the measurements as “left” and “right” for each
    measurement of the label.6)     
    Do a probability plot broken out by left/right and you will
    see the lurking problem. The distribution of each measurement subgroup is much
    tighter than then the overall dataset. 

     

    N

    Mean

    StDev

    Cp

    Entire set

    40

    1.9738

    0.4046

    0.42

    Left

    20

    2.3100

    0.2468

    1.36

    Right

    20

    1.6375

    0.1970

    1.25

    7)     
    When you use the entire dataset, you have two normal
    distributions on either side of the target that combine to make a wide,
    somewhat uniform distribution. It is well centred, but wide because you are
    combining both left and right measurements.8)     
    The sum of the two measurement (left and right) is fairly
    constant, as you would expect.9)     
    The difference of the two measurements, however, shows a clear
    trend, the centre of the labels has drifted 0.90 mm from the beginning to the
    end of the run. Send me an email address to [email protected] and I can send you
    the entire session file from Minitab14. Cheers, BTDT

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    #139754

    PH
    Participant

    Thank you – I’ve sent you an email.
     
    PH

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    #139760

    better than darth
    Participant

    Cp only focuses on the process spread without considering the spec limits. Compute for Cpk to see how it fits with the spec limits.
    Also, you may want to check how you have gathered the data. It must not combine apples with oranges, only for those with same parameters.
    Aside from that, check the normality of the data, it seems not to be normal.

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    #139762

    tottow
    Member

    Dear better than,
    Before answering a post with a screen name which insinuates you are better than someone else, maybe you should try reading the other posts in the thread, so your answer is not just a regurgitation of information others have already posted.
    Just a thought.

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