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DOE noise characterization and incorporation.

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  • #45352

    Ward
    Participant

    I am running an experimental design for an abrasive cutting/grinding process and have run into a small hitch that me scratching my head. I have been lucky enough to not have to worry about this situation with other DOE’s performed in the past, but in this process I believe the noise is critical to process characterization and optimization.
    What I am seeing is the decay of cutting efficiency in a dicing blade (diamonds imbedded in a metal matrix) over the course of use, which I am considering a noise factor in controlling the process. However, I am forcing wear issues into the process since my DOE is working/wearing the blade differently depending on the process factors I am changing. As a result, I am facing a spent blade only a couple of runs into the DOE, which means I will have to change the blade out and use a new blade.
    My question is this: How do I take blade wear (noise?) into consideration for a DOE while maintaining legitimate results for each DOE run? If I run the existing blade for the remainding runs, I will surely get skewed results.
    Thanks in advance,
    Pete

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    #147998

    Eric Maass
    Participant

    Pete,
    You have an interesting challenge – and your perception seems right that the decay of cutting efficiency is critical.
    You might want to have two responses – the response you were going to use, and the rate of decay – each as a function of the factors in your DOE.
    In that case, although it might be somewhat expensive and could be complex in terms of logistics, one approach would be to designate a set of blades for each run or set of trials in your experiment, and do several replications for each run.  Then, you would use the same designated blade each time you would replicate that run. You could then analyze the decay in performance using that blade as one of your responses.  Best regards,Eric

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    #148003

    Robert Butler
    Participant

      If you are able to completely randomize your runs over blades then this shouldn’t be a problem. The variation due to blade wear will not be confounded with any of the variables in your design and will show up only as an increase in the resudial error (random noise).
      If this isn’t an option then you will have to give some thought to your design construction/run allocation.

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    #148005

    Ward
    Participant

    Thanks for the responses.
    Eric: Decay is a very difficult and unreliable response to measure, since the wear is very subtle, but leads to pronounced differences in other responses. We are working on throroughly characterizing the process, but have yet to get to this level of detail. Additionally, blades can run as much as $150/ea., which might lead to an extremely expensive DOE. (Yes, I  know, sometimes the upfront $$$ is worth understanding and optimizing…no argument there.)
    Robert (Bob?): I was thinking that randomization would take care of these issues, though I was intimidated by the prospect of missing something critical. I am using a full factorial design with a 2-level categorical, and 2 3-level continuous factors, with no center points and no replicates for this DOE. Also, I am using JMP if that helps in the discussion.
    I am also wondering if this wouldn’t be a good place to use blocking? I have never really delved into this area of DOE, so I may be talking out of my backside.
     
    Thanks again,
    Pete

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    #148008

    Robert Butler
    Participant

    Based on your description I don’t see that there is anything to miss.  You have a variable – blade wear – which you can’t control and you want to make sure its effects aren’t confounded with any of your design variables. 
      The point of randomizing a deisgn is to insure that the effect(s) of any uncontrolled variable(s) is/are not confused with the effects of the variables in the design. I wouldn’t recommend blocking for the simple reason there doesn’t seem to be any need for it.
      If you can randomize across blades and it turns out that blade wear is THE big hitter with respect to your process what will happen is that the residual error will be so large that none of the variables of interest will test as significant.  As I’ve mentioned in previous posts on this subject, if this happens, your design will have been a success and you will have some very valuable information about the process.

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    #148011

    Dale
    Participant

    It sounds like this is an existing process.  if so, why not look at the production data using a residual analysis?  A deterioration of the blade should show in that analysis.

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    #148012

    Robert Butler
    Participant

      In re-reading your post I realize I overlooked a point.  You mentioned you weren’t doing any replicates.  I realize designs are built with time and monetary constraints, however, if it is at all possible to replicate even one of the design points I would recommend doing it. 
      A good choice for replication would be to start with a new blade and choose any one of the design points that had been run at the end of one of the previous blades useful lives.  This would be a particularly effective contrast since, while the blades would be different you would have a measure of the impact of new vs. old for a single design point and the resultant difference could be treated as a measure of pure error.

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    #148015

    Chris Ely
    Participant

    I am fairly new to some of the advanced DOE techniques in use but this seems like it may be a likely candidate for a Taguchi robust design DOE. Could you use several saw blades with varying degrees of wear in the outer array?
    Sorry this isn’t really an answer as much as a question. The use of an outer array seems to fit here though and I’m hoping for feedback about this design style.

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    #148016

    Robert Butler
    Participant

       This is where Taguchi’s re-definition of the word “noise” and the statistical definition of “noise” can cause a lot of confusion.  Taguchi’s “noise” consists of variables you can control but really don’t want to.    The kind of noise Pete is facing is real noise – uncontrollable but capable of being confounded with an existing design parameter. 
      To your point – Pete indicated the degree of wear is going to vary depending on DOE conditions – Taguchi’s “noise” variables don’t permit this kind of variation.  With his designs you take one of the renamed saturated factorial designs and run this complete design at each point in his “noise” array.  In order to do this you would have to have a uniform pile of “worn” blades each with the same degree of wear and a pile of new blades (to correspond to the -1 and 1 levels of the “noise” matrix.
     You would then run each design point of the “inner array” DOE at the “worn blade ” condition and then at the “new blade” condition. The execution of this effort would insist on a one-to-one correspondence between blades and design points – that is, if your “inner array” consisted of 8 points you would have to have 8 new blades and 8 worn blades for a single execution of his design.
      At the end of such an effort you would have spent a lot of time and money and you really wouldn’t have any information concerning the effects of the DOE variables of interest in the presence of “real noise” which is what Pete is actually interested in knowing.

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    #148021

    LJ
    Participant

    Robert:
    Have you attended any Taguchi Training by ASI?

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    #148022

    Robert Butler
    Participant

    No I haven’t LJ. 

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    #148025

    LJ
    Participant

    I believe Taguchi treats problems like the one described as a ‘dynamic’ DOE, but I’ve not seen this distinction in any previous posts..
    I just wondered if there was anything in conventional DOE that correponded to a Taguchi dynamic problem, such as a steering box design. Perhaps a conventional DOE would just consider the pointing of the steering wheel to positions m1, m2, m3, as a three level design. I don’t know.

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    #148026

    Chris Ely
    Participant

    Robert,
    Thanks for the valuable information.
    I have another question that you may be able to answer: When running a robust design study do all “noise” factors in the outer array need to be completely controlled? For example, if temperature is the noise variable  I want my process to be insensitive to, can I use “less than 50 degrees F” as my low (-1) and “greater than 80 degrees F” as my high (1)?
    I think this is probably unacceptable but would like to hear your thoughts/experience on the matter.
    Thanks again

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    #148027

    Eric Maass
    Participant

    Pete,
    Yes, I suspected that the new blade approach might be too expensive.
    Here is one more set of suggestions:- Since wear “…leads to pronounced differences in other responses”, consider using one or more of those other responses – and the change or variation of those responses – for analysis.- As Bob mentioned, you might reconsider your decision to go without replicates. You might be able to use the replicates to obtain insight into which factors have a big impact on wear and thus the other responses:  run the DOE with one new blade, then re-randomize the order and run the DOE again with both the now-used blade and another new blade. Then perhaps run it a third time, with a new blade, the just-used blade, and the original blade.I think that the standard deviation of another response (that is sensitive to wear) among these replicates could be analyzed and could provide insight into which factors increase your sensitivity to the “noise” of wear.As part of the analysis, you would have the opportunity to analyze some differences – the differences between new and used blades, the differences between the first time a blade was used and the second and third time the same blade was used with the same settings / set of factor levels.
    Best regards,Eric Maass

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    #148028

    Robert Butler
    Participant

      Based on my understanding of Taguchi’s definition of “dynamic” I don’t think this is the same situation.  As I understand it the concept of dynamic consists of setting up a design to permit the identification of an optimum that can be applied to a variety of process conditions. 
      In the instance of the steering box this would seem to imply building a design so that you could either identify an independent optimum with the steering box at either position m1, m2, or m3 or identifying some compromise optimum that would be the “best” setting for minimizing the effects of steering box position on both the mean and the variation of the measured response.  Implicit in this definition is fact that the setting doesn’t have a “memory”.  That is, when I go back to a setting of position m1 after having run one or more other settings the results of the test at m1 will not depend on prior tests.
      Pete said, “However, I am forcing wear issues into the process since my DOE is working/wearing the blade differently depending on the process factors I am changing.”  My understanding of this sentence is that he cannot pre-set the wear and then run a design rather, his wear is actually a function of the DOE parameters and will change as the parameter settings change which means the blade wear will have a memory.  Since the blades are going to wear and since he can’t control wear amount and type in the production environment he’s going to have to  “scramble” the memory to make sure it isn’t impacting his experimental results. The only way I know to do this is to randomize.
      To your point – I believe you are correct. In a regular design you would pick the three steering wheel positions and use them as levels in the design.  The predictive equation could then be used to identify optimum settings for the response to a particular steering wheel setting or to identify the best compromise setting for all steering wheel positions. This, of course, only addresses the impact on the location of the mean response. In order to understand the impact of the design parameters on the variability of the response you would need to run a Box-Meyers analysis on the results of the design.

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    #148031

    Robert Butler
    Participant

    Chris, yes and no.  What you are referring to is the issue of the “fuzzy X’s”.  You can choose to have the low and high settings as you described but if you do this you will have to record the actual value at the time you ran any given experiment and you will have to use that particular value in your design matrix.  If you don’t do this and if you just call anything less than 50 degrees a -1 and anything greater than 80 degrees a +1 the machine will assume all of your low settings are identical and all of your high settings are also identical and run the analysis accordingly.  The end result will most likely be garbage.  The post below discusses this issue in more detail.
    https://www.isixsigma.com/forum/showmessage.asp?messageID=96473

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    #148037

    LJ
    Participant

    Many thanks for your detailed reply Robert.
    I found the grinding example of particular interest because I’ve worked on several grinding processes – the most challenging was a large cantilever router used to grind a large bore. Why it was horizontal instead of verticle I have no idea?
    The reason why I suggested there might be a similarity between grinding and a steering wheel is because the cutting rate of a grinder isn’t just a function of the cutting wheel, but is also a function of the cutting rate – the pressure applied behind the spindle.
    However, the main point of my post was to find out whether or not there is a conventional DOE approach equivalent to Taguchi’s dynamic design. Just to confirm, my understanding is there isn’t – except to treat each signal level as a separate DOE.
    Thanks!
     

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    #148038

    Robert Butler
    Participant

      LJ, I think we are talking past one another here. You don’t treat each signal level as a separate DOE you treat them as levels of a particular variable within a single DOE. If the signal has separate aspects to it and if these aspects are separable you can treat them as X different variables within a single design. 
     As far as I know there isn’t anything a Taguchi design can do that a “traditional design” can’t do as well.

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    #148068

    LJ
    Participant

    Thank you for identifying a clear difference between a conventional DOE and a Taguchi design.
    Perhaps there is a good reason why Taguchi takes a different approach – as yet unappreciated :-)
     
     

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