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Nested ANOVA

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  • #37762

    Lala
    Member

    We have 6 different types of cutting inserts to be tested for performance (part diameter variation) on a single CNC turning center. We need to check for part variation at New, Middle & End life of each insert also.
    Are we correct to setup an nested ANOVA? Please advice. How would I select my model terms?
    Thanks.

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    #111857

    Lala
    Member

    To the attention of the forum.

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    #111895

    Robert Butler
    Participant

    The short answer to your question is no. ANOVA is a test on means not a test on variation.  Your post indicates your interest is the quantification of part variation at the beginning, middle, and end of the life of the tool.  Your post suggests the following:
    1. You have one CNC machine
    2. You have six different types of cutting inserts
    3. You would like to quantify manufactured part variation at three stages of tool life.
      Questions:
     1. What is the nature of the difference between the tools?  Same tool, different manufacturer, different tools, same manufacturer, different tools, different manufacturers or?
    2. What is your definition of middle and end of tool life? – Number of parts made, hours on machine, active hours on machine, or?
    3. For tool testing what are you proposing to do? All tools make same cut, all tools make cut appropriate for their particular application (assuming they are not all the same tool type). All tools cut same kind of material, tools to be tested over a variety of material? etc.
    4. What is the procedure with respect to treatment of the tool over its life. Does it receive periodic re-sharpening as it moves through its life cycle? Is it a use once and discard? or?  If it does receive periodic sharpenings, how do you determine when it is needed? 
      You will need to tell us more about the purpose of your test before I or anyone else can offer suggestions concerning the kind of tests you might want to perform. 
     

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    #111899

    Nanni
    Participant

    Robert,
     
    The ANOVA is not always a test on means. When the model has random effects (Model II), the ANOVA is a test on variance. If you need more information I recommend you this book:
    Searle, Shayle. “Variance Components”.
     
    Regards,
    Nanni
     

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    #111903

    Lala
    Member

    The inserts are made from different compositions & geometry by the same manufacturer. These inserts are used for hard machining. The production rate is about 500 parts per hour. The experiment is planned on new inserts.
    The new, middle & end life of tool means the condition of tool. If a tool life is declared as 4000 pcs, above terminology identifies the condition of tool nearing @ new, 2000 & 3500 pcs.
    Thanks in advance. 

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    #111971

    Robert Butler
    Participant

    As you describe it I don’t see anything in your study that is nested.  The comparison seems to be one of asking questions about the six different tool types. 
     
      One possible way to test each tool would be to take X number of samples of the output when the tool is new, X samples when the tool has made approximately 2000 parts and X samples when the tool has made around 3500 parts.
     
       If you simply sample X when the tool is new, X when the tool has made around 2000 parts, and X when the tool has made about 3500 parts the results of measurements within each time frame will probably not be independent so your estimates of variability at those part quantities will probably be less than the actual variability. Consequently, in order to do your test and have meaningful estimates of variance you need to know that your samples are independent. 
     
      If you have access to Minitab or its equivalent you should set up your standard tool and, for one run make a special effort to take the pieces as they come off the machine and identify their time order.  I realize that at 500 pieces an hour this will require some special effort on your part but it is a one time thing and the knowledge you gain about the degree of separation you will need for sample independence will be worth it (and yes, I’ve done such things in the past). Next take you measurements and run a time series analysis on the results.  From this you will be able to determine the separation between parts needed in order to guarantee sample independence.  
     
      Randomize the order of testing for each of the tool types and run one per day taking your independent samples (500 pieces an hour for 3500 pieces works out to about one tool test per day).  When you are done, use one of the multiple variance comparison tests to assess variance homogeneity – you will be looking at differences between tools within a wear interval and across wear intervals.
     
     

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    #112010

    Lala
    Member

    Time series analysis is not entirely convincing. Test of equal variance would be a better option (?)
    Yes. I have MINITAB 14.
    Sunil.

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    #112016

    Robert Butler
    Participant

      You don’t use the time series to assess the variance. You check your data using a time series to make sure the samples within a given time period for a given tool are independent. If your samples aren’t independent your estimates of sample variance will not reflect the actual variance of the system.  With a machine turning out 500 pieces an hour you might find you have to have a separation of 100 pieces between samples in order to guarantee independence. On the other hand it might be as little as 4 or 5.  The only way to tell is to run the test.
      In re-reading your posts I noticed you said
    “The inserts are made from different compositions & geometry by the same manufacturer”.
      Is there any chance you can quantify the composition and geometry?  For example if the composition is a change in the ratios of the metals in the alloy and if the geometry could be classified with respect to things like the pitch angle of a cutting edge then you have the potential for doing a lot more than just assessing changes in variance as a function of six levels of a type variable – you have the possibility of examining the problem from the standpoint of a designed experiment and also from the standpoint of having to check fewer inserts.

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    #112019

    Thaly
    Member

    Sunil,
    Unless you want to include the suppliers of the 6 variety of inserts as a factor, it is not a nested ANOVA.
    You could just do a general full factorial design. One thing to note is that your experiment looks like it could be affected by not randomizing the experiment, since running that many parts might amplify a lurking variable and might influence the later part of the experiment. you’d be the best person to decide if you need to randomize the runs.
    It is best to replicate the experiment in a different order and compare the results. if there is not much difference, you could remove the block SS and then you would have values which would be a statistically more significant than one.
    Hope this helps

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