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Cpk Combined vs Individual Cavities

Six Sigma – iSixSigma Forums Old Forums General Cpk Combined vs Individual Cavities

This topic contains 16 replies, has 11 voices, and was last updated by  F. Barros Brazil 13 years, 7 months ago.

Viewing 17 posts - 1 through 17 (of 17 total)
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  • #42614

    walden
    Participant

    On multiple cavity tools I always calculate the Cpk for the individual cavities, instead of using the data of the combined cavities. I realize that theoretically all the cavities should be the same, but I’ve rarely seen this in my experiences.
    My thought is that in order to combine data from all cavities you need to show through the appropriate statistical tests that the means and variances between the individual cavities are not significant. I’m curious to hear the opinions of others on this subject and whether you agree or disagree.
    Also, when control charting (Xbar R), if subgroups consist of one part each from all cavities, can this actually mask process variation and artificially inflate the calculated Cpk since you’re then plotting the differences between cavities?

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    #134743

    walden
    Participant

    Any help or comments would be appreciated.

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    #134760

    Seaotter
    Member

    Chris,
    I would agree that if there is no significant difference through the cavities (for whatever parameter), then the data can be combined to give a ‘tool’ Cpk. Expanding on that, even if there are significant differences but each cavity is in control, you can also do a combined ‘tool’ Cpk.
    Hope that helps,
    Seaotter

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    #134763

    Seaotter
    Member

    Chris,
    I’ve been thinking about your second point. If there is higher variation between cavities than within them, this would increase the overall distribution and decrease the Cpk.
    Seaotter

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    #134764

    walden
    Participant

    Seaotter,
    I appreciate your response. That is exactly the situation, the between cavity variation is typically greater than within cavity variation. I have seen combined cavity Cpks of 0.50, however each individual cavity Cpk could be greater than 2.0.
    My main concern is the effect of combining these cavities on a variables control chart.
    Thanks again,
    Chris

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    #134765

    Andejrad Ich
    Participant

    Chris,
    I’ll imagine we are talking about a multi-cavity mold tool.  If you have USL and LSL for individuals coming out of that tool and your Ppk is 2.0 or greater, then do you really care if there are differences (even statistically significant differences) between cavities?  I mean….so what?  Lets say your capability-by-cavity analysis reveals differences — will you retool/adjust the troublesome cavities until they fall in line?  Will you block off those cavities?  Again, the answer is….as long as the overall population of output product is highly capable, then you will run the tool as is and the effort to run/track/chart individual analyses by cavity is really of no value whatsoever. 
    If, instead of Ppk of 2.0 or greater, you are in a marginal capability situation and you NEED to identify and eliminate sources of variation, then you may logically conduct a capability-by-cavity study (then you still have the problem of what to do with the information once you have it).  The only other time(s) you might want to bother with such an analysis would be in initial acceptance/qualification of a new tool or to check what you believe may be a worn tool (but you will STILL have the problem of what of any use do/can you do with the information).
    Generally, a capability study should be of the overall output of the 24 cavities (e.g.) all producing output with each machine cycle.  That is really the population of parts being piled up at the output of the process.  Is that output capable or not?  Variation showing up in samples of 5 parts collected (for charting) from the pile generated by 24 cavities will be captured/reflected as a source of normal variation already reflected by the chart limits. 
    Andejrad Ich

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    #134802

    Seaotter
    Member

    Andejrad,
    I thought that Ppk was based on the overall variation of the process. Process performance vs. process capability (Cpk). Chris’s suggestion is that his Cpk can be as low as 0.5, so his Ppk would be lower than this?
    This being the case, surely he needs to determine the cause of across tool variability and reduce it as any value for either Cpk or Ppk of less that 1.0 shows the process is worse than marginal.
    I thought that process control was a means of continual improvement. I agree that the study should be of the tool as a whole (the parts being piled up at the output of the process), but I would disagree that collecting 5 samples out of 24 and charting that will show the true run of the process.
    I would gain an understanding of where the variability arises and deal with the causes of that. Once this is reduced then sampling across the tool for charting purposes would be acceptable. If individual cavities are not significantly different from each other, as they must be at the moment, a useable SPC chart can be employed and any increase in variation will be quickly identified.
    I’d be interested in your views.
    Seaotter

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    #134808

    walden
    Participant

    Seaotter,
    I think you and I are on the same page. Unfortunately, I haven’t been able to respond to Andejrad’s post until now.
    I agree with Andejrad that based on the excellent process capability of the individual cavities I wouldn’t retool, make new cavities or block them. Obviously the output of the process is more than acceptable.
    However, I disagree that a capability study should be of the overall output of all cavities. (Andejrad, I assume you mean to calculate Cpk of the combined cavities). If you have a number of different cavities that are known to have significant differences in their means, any calculation of summary statistics and/or process capability of the mixture of these populations into one big population is incorrect. Surely it can be done, but isn’t it meaningless? Would you mix the output of several machines running the same part and calculate Cpk? I would hope not.
    As far as control charting, if you are pulling random samples from a mixture of cavities known to be different, aren’t you plotting cavity to cavity variation instead of process variation? Does an out of control point mean the process has changed, or just that I picked the wrong combination of cavities in my sample?
    Cheers,
    Chris

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    #134812

    Dartman_underseige
    Participant

    Chris,
    In real life, no process are the same. Thus, no identical items will be the same.
    Engineers needs individual capability index measurements per cavity for control and improvements.
    Your BOSS needs over-all plant capabilty index per process for customer requirement perhaps.
    You are paid to satisfy both. Therefore, you need to do both eventhough you feel other data have no sense to you at all. Use the only data that is right and needed for your calculation. Unless your the boss.
    Hope you get my point:
    Dartman_undersiege
    Message Assumptions: Chris is not plant BOSS. He’s just engineer.  
      

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    #134850

    walden
    Participant

    Dartman,
    Point well taken. Like the old saying, he may not always be correct, but he’s always the boss.
    Thanks again,
    Chris

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    #134857

    Chris Butterworth
    Participant

    Hi Chris,
    With a Cpk of 0.5 you are losing a lot of money and your boss would like to know how to stop this. You already know that it is cavity-to-cavity differences. I would suggest further analysis is of low value and the next step is retooling or blocking off the offending cavity(ies).
    Chris

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    #134866

    Marc Richardson
    Participant

    Let’s pull this one down to the ground for a minute. Let’s say you have a 4 cavity mold with the following Cpk values:
    Cavity A: 1.45
    Cavity B: 1.53
    Cavity C: 1.76
    Cavity D: 1.37
    Combined, the over-all Cpk is .9. If you ship the product, will your customer receive product within his/her capability expectations? If you work in the automotive business, the answer is yes. Combining the distributions simply inflates the capability index.
    Now, the key word above is capability. If monitoring process variation is your goal, than combining cavity data is definitely what I would do. In this case, we want to understand cavity to cavity variation and time to time variation. If there is nonrandom variation in the process that effects all 4 cavities at once, I want to detect that. If, however, a vent plugs up in cavity B, I want to detect that.
    One way to set-up the chart is to assign each cavity a position on the chart. For example, cavity A will always appear on the first row, cavity B on the second row and so on. Now, when the vent plugs up in cavity B, I will see a signal on the range chart. If the weight of all the parts increases at once, I will see a signal on the average chart. This arrangement also allows you to run a Individual & Moving Range Chart on each cavity/row data to narrow your search for an assignable cause.
    Marc W. Richardson
    Sr. Q.A. Engineer
     

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    #134868

    Dartman_undersiege
    Participant

    Marc,
    Would this makes the life of us engineer more difficult if you wanted us to use a combine the data ? This would means we need manipulate our data further, right??
    Since, we are getting the Capability index per cavity, whereas I believe using the same specification limit, would it be much simpler if we just provide adjustment on the lowest Cpk index (in your example Cpk=1.37) and centering it to the specification. If this one improved, then over-all capability index goes up right??.  You can easily detect improvement if its not combine as well as preformance drift.
    Other than over-all plant performance report is concern, I don’t see a clear use of Capability Index combine data. At the end, you will explode it to dig further.
    We engineers believe on a K.I S S approach.
    Keep It Simple (Stupid).
    Sorry for the word. Just my one cent comments.
    Dartman_Undersiege (Dilbert’s)

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    #134948

    Ronald
    Participant

    In a previous life as a Supplier Quality Engineer, I ALWAYS stated, either upfront in a qualification requirements document, or in a control plan, how I wanted my suppliers to evaluate & monitor capability.  During qualification of a new multi-cavity tool, or for reparis/major changes to an existing tool, I always required cap studies for each cavity.  If significant differences were seen cavity-to-cavity, I, as the customer, would likely be at risk from part-to-part variation due to parts coming from different cavities; thus, corrective action to reduce this variation was my requirement.  Relying on a combined Cpk without such information is dangerous.  If there was no significant or meaningful difference observed, capability was acceptable, and the tool was approved, I often selected the worst-case cavity (i.e., lowest Cpk) as the one for on-going SPC, with periodic evaluation of the other cavities, to ensure cavity-to-cavity variation did not become excessive.  Only then would I approve combined cavity capability evaluation. 
     
    So, my recommendation is to first discuss this with your customer.  Make sure you’re aligned with what they need, but also understand the financial impact to your business by potentially scrapping acceptable product.  As another poster correctly stated, an observed difference may be statistically significant, but not meaningful.  Don’t guess – talk with your customers!
     
    Also, I didn’t see any other replies asking a basic question…. Did you do a GR&R, and what were the results?  As you probably know, if your measurement system is not good, your capability analyses will be questionable, and this entire discussion becomes secondary.

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    #135014

    Mikel
    Member

    Chris,
    I faced this problem with a liquid filling machine with multiple filling heads.
    Go to the web and look for Stochos, a statistical software and consulting firm. They write newsletters and wrote one a few years ago that addresses this problem exactly.

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    #135138

    AT
    Participant

    Dear Chris,
    In order to test the significance in difference between the 2 groups use 2 sample t test for means and f- test for variances. If p value is less than 0.05 in both the cases, then there is significant difference between the groups perfromance.
    If more than two groups (Cavities) are there, use ANOVA and conclude which are belongs to similar family by comparing the p value among the individual cavities
    Regards,
    Ramesh Patnana
    LS expert
     
     
     

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    #135211

    F. Barros Brazil
    Participant

    Chris/Stan,
    There is a good discution here,
    We also faced this problem with liquid filling machine with 6 heads. Firstval we performed studies to each head to know better the process – we would like to use SPC in Group (see Montgomery, Introduction to SQC – 9-3.2 Ed 4a.), but the variation among heads were so big, then we decide to control  heads separated using Xbar-R Charts.
    In other case, we have a machine with 30 “cavities”. In fact there is a tablets compresson machine with 30 stages. First problem: there is no cavity identification, and it’s impossible to get it. In this case we began the study using Xbar-S chart. We are taking 30 sequencial samples per subgroup, but we don’t kown where each tablet come from. In fact it is a large sample. Another problem: it’s a short run. We get only about 15 samples per lot.  We are in doubt if we can use sample size of 5 in subgroup and use a Xbar-R chart, if the standard deviation within among stages is knowing…
    Anybody have any suggestion?
    Regardin this, Montgomery refered to Ott and Snee (1973) “Identifying Useful Differences in a Multiple-Head-Machine” – Journal of Quality Technology, but a can not get this paper.
    Thanks,
    F. Barros
    (sorry poor english)

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