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I-MR or X Bar and R Control Chart?

Six Sigma – iSixSigma Forums General Forums Tools & Templates I-MR or X Bar and R Control Chart?

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  • #236283

    Karim Mohsen
    Participant

    If I had about 30 samples obtained from one batch produced in certain time and under same condition, which is better to use I-MR chart of X bar & R chart?

    And which chart should i use if i had 30 results from 30 different batches produced in several days ?

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    #236293

    Robert Butler
    Participant

    If by a batch you mean a single run such as contents of one reactor vessel then the answer is neither because those samples are repeated measures – not independent measures. If you try to build any control chart with that kind of data the control limits will be too narrow because the sample-to-sample variability within a single batch is going to be less (and possibly much less) than batch-to-batch variability.

    As for the second question concerning 30 results from 30 batches – the question you need to answer is this: Is there any obvious subgrouping of the measures? If there isn’t then forcing what amounts to single measures into some artificial grouping is of little value. In all of the cases I ever dealt with where the output was a batch of material I used IMR charts and never had a problem.

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    #237094

    Chris Seider
    Participant

    I’d ask you to consider why you’re looking to use SPC.

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    #237095

    Karim Mohsen
    Participant

    @cseider
    it is customer request , to do the capability and the control chart of 30 samples from different 6 batches each

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    #237096

    Robert Butler
    Participant

    So, is it a total of 30 samples from 6 batches for a total of 5 samples per batch or is it a case of 30 samples from each of 6 batches for a total of 180 samples?

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    #237098

    Karim Mohsen
    Participant

    @rbutler

    30 sample from each batch for total 180 samples , he wants to run the capability and control chart for each batch

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    #237099

    Robert Butler
    Participant

    As I said in my first post – the problem is that of sample independence. If your batches consist of something like widgets stamped out on a production line then you would need to first take as many samples as you can at a uniform time interval for a single batch and run a time series analysis to determine the minimum separation in time between samples needed to declare that the samples are truly independent of one another and then take samples at that time interval or at some time interval greater than the minimum and look at the number of samples per batch this approach will provide and use those to compute your Cpk.

    If you can’t do this then you will have to take the time to understand the issues associated with control charting and calculation of Cpk in the presence of lack of independence of measurement (auto-correlation). As Wheeler and Chambers note in their book Understanding Statistical Process Control 2nd edition – there is a myth (see pp.80-81) that the data needs to be independent before it can be control charted. As they note- you can use auto-correlated data but there are issues and things you need to keep in mind.

    If the batch is something like a large reactor vessel then the multiple samples per batch will not be independent and auto-correlation is guaranteed.

    As for a Cpk with auto-correlated data you should borrow a copy of Measuring Process Capability by Bothe through inter-library loan and read pages 781-792 – the chapter subheading is 13.3 Processes With Auto-Correlated Measurements. In short, if the batch samples are not independent you will need to do some reading to gain an understanding of the issues before you try to build and interpret a control chart or calculate a Cpk with this kind of data. For both issues, control chart and Cpk, I would recommend the section in the Bothe book as a good starting point.

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    #237142

    Chris Seider
    Participant

    This makes SOME sense if the batches aren’t homogeneous OR if the batches are changing over time after completion of a step or after final approval.

    Six batches only would make me ask why but you must satisfy the customer of course.

    However, i don’t understand 30 samples from each batch and making a control chart of X-bar for 6 means. I hope the samples are cheap to sample and test but I would think you’d find more interest in 6 samples for 30 batches or even fewer samples.

    Be aware that process capability using SPC isn’t as good as doing your Cp/Ppk/etc. analysis of the individual readings–capability analysis on means is the wrong approach.

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    #237173

    Karim Mohsen
    Participant

    @cseider

    but i think that 6 samples are too few to do capability analysis ,or do you mean to combine the all 6 samples of the 30 batch in one capability analysis and one control chart ? if you mean this so , it will be more reasonable than that the customer want , the only disadvantage of this is that it will take very long time to achieve and in this case it is better to use X bar and R chat , right?

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    #237174

    Chris Seider
    Participant

    How many batches do you produce annually? I wasn’t say you must have 30 batches but data from 6 batches would seem too few.

    Biggest question you should consider with your customer–are the batches fairly uniform (after completion)? I’d be just as interested in knowing my process capability with the many sources of variation so more batches than 6 would seem appropriate UNLESS you have so few but as @rbutler and I have indicated–30 samplees for 6 batches seems like oversampling if you want to understand your variation within the batches with not much data about your variation between batches.

    Doing an x-bar chart on 6 means would seem to be silly unless required by your customer as a minimum but would encourage more. Be sure they aren’t asking for 6 samples amopngst 30 batches would make more sense. I’m NOT advocating needing 30 batches but am trying to reconcile your statements about the customer needs. Heck, even 20 batches would give you a good picture of variability between batches if it’s practical.

    Please consider that running X-bar R charts isn’t a capability analysis but running a capability analysis on the individual readings from x samples/batch is more of one. If you are unclear about variability within a batch, then do your 30 samples on one batch and see what you see before even doing the other 5 batches.

    Basically, we’re saying be clear what your customer wants and also we’re clarifying X-bar R charts and process capability give you differing snapshots for your process. Have you confirmed you have a good gage? This would all be a waste of time if you haven’t confirmed precision and accuracy.

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