DOE and spefication Limits

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    Jose Ramon

    Hello Professional of Six Sigma.
    I have a consultation about DOE and specification factor limits. I have one equation and just change the factors specification limits (Minitab 15):
    1).Y =  60-4.63A + 6.38 B + 31.75 C + 14.38 D – 17.25 A*B – 26.25 *A*D + 19*B*D +7.88 C*D – 14.25*A*B*C- 23.25*A*C*D + 11.75*B*C*D
    2). Y =  60-4.62A + 6.38 B + 31.75 C + 14.37 D – 17.25 A*B – 26.25 *A*D + 19*B*D +7.88 C*D – 14.25*A*B*C- 23.25*A*C*D + 11.75*B*C*D
    3). Y =  60-4.62A + 6.37 B + 31.75 C + 14.38 D – 17.25 A*B – 26.25 *A*D + 19*B*D +7.88 C*D – 14.25*A*B*C- 23.25*A*C*D + 11.75*B*C*D
    I change the specification limits 3 time that why I have 3 equations. But for example, I use the first limits for A (518,600) in the second equation A(600,900) and in the third equation A(900,1200) The questions are:
    1) If I change the spefication limit this mean that I am analyzing difererents regions of .the whole area right ? How This affect the calculation of Y( output ).  If you see the 3 equations in the 2nd change 2 numbers ( from -4.63 A to -4.62 A) and (from -14.38 D to -14.37 D).  In the 3rd equation change just 0.01.
    The equation could have max. range limits ?
    The final Y ( output ) could change to another direction if I continue changing the limits right ?, Does this mean If, for instance the specification for A (900,1200) and the customers want (400,500), Could I run the experiment for this region just changing the specification and see what happen ?
    Please let me know ab out this.  Thanks so muck for you help and advice. 
    Happy New Year 2008.
    Jose Ramon


    Robert Butler

      You will need to clarify some points.
      Are you saying you built three different designs and generated three different equations for a particular Y or are you saying you built a single design where A was allowed to have 4 levels (518, 600, 900, 1200) and you are taking subsets of the design space and building equations for each region?
       If it is the latter then you are doing the analysis incorrectly and if it is the former then I doubt there is any significant difference between the coefficients for A and for D – use the standard errors of the estimates of the coefficients to check this.
      If it is the former I’d be curious to know why you had to build three different designs and couldn’t just use a single design to check the region of interest.


    Jose Ramon

    Mr. Butler thanks for your comments.
    In fact, I built 3 different equations with different specificactions all of them.
    I built separately becuase They are for different departments and the data is different for all.  This mean that A for Y1 is different than A in Y2 and y3.  Now the question is the same.  If I change the region in one equation what happen ?.  There is a region that I cannot cover with an equation or I can use whatever I want ?.
    Another question:
    Let`s say we have Y ( response ) and that I replace all A,B,C,D combinations that I have .
    The equation is: Y = 36.75 – 0.87 *A – 8.62 *B + 1.63*C + 1.63 *D – 8.25*A*B+10.50 *A*C – 16.13*A*B*C + 10.12
    when I replace all coded values for this equation I get:
















    Let` s us say this is time.  The max. time is 74.74 and the lower time is 3.26.  With one optimize, minimize and maximize this equation ?.  I use the main effect plot to get an answer but I think I am making a mistake . The main effect give me what factor affect more to the output but This is a good tool to get the Optimum output ?.
    Thanks so much for your help
    Jose Ramon


    Jose Ramon

    Mr. Butler always thanks so much for your comments and help.  I would like everybody in this Forum do the same.
    I have a couple of questions:
    1. If I perform a DOE and your output give you this outputs:
    Y = 53.4, Y = 56.5 , Y = 78.98 , Y = 98.19, Y = 100.75
    and the factor are A ( 560, 300) …this is the number of customer is A departments in the mornign and in the afternoon. (of course I have B,C,D factors).   A professor in Japan ask me this question:
    If in your model you are testing A (560,300) sec in the department A, B (1,3) staff in the department B, and C(15,60) sec C = time to finish an order in the department C and your output is the whole waiting Time  .  Y mean whole waiting time considering A, B,C.  What happen If one day 800 persons come to be attended ?.  If you tell me than 1 person is O.k what happen If the customer increase ?.
    Mr. Rubert How can I demostrate this ?.
    I tried to do it calculating manualy.  I undetand that DOE with give you an answer for a range but If this range is not cover, this means than I have to answer that the waiting time will be longer but how longer ?.
    Please let me know who to solve this problem out ?.  What is your opinion ?.  am I wrong?.  Please let me know.
    And thanks a lot



    Robert may reply and answer this more thoroughly, but here is my two cents worth.
    In general it is inadvisable to extrapolate prediction equations from DOE beyond the region tested. I have sometimes allowed myself to do this within about 5% of the factor limit. This is with physical systems whose characteristics are somewhat well understood. With a system involving humans responses;as this one does, I’d be less inclined to do so.
    The reason you do not want to extrapolate beyond the tested region is that you really have no information as to the response surface in the extrapolated area. There may well be a “cliff” there. For instance, perhaps 800 customers will not be able to fit inside the department, causing a queuing and resultant time changes as they go in and out the door.
    Stick to predictions within the region tested or go out and get more data in the region of interest.


    Fake ATI Alert

    It  seems  that  you  are  an  expert  in DOE
    Can  you integrate DEO with F & T-Test?
    If  Yes ,can  you  elaborate  through  a  simple  example?
    Thanks  and  Regards


    Jose Ramon

    To: Mr. Robert and Mr. Daves
    I understand that the DOE has a region. Now the questions are:
    1). If we have 3 departments A ( 2,3)persons, B(2,4)persons, and C(1,2)persons and the output is waiting time.  If my optimization DOE express that A = 2, B = 2 and C = 2 give me the lower waiting time Y = 60 sec.  How can I say to the Top Management ( for instance ) that if they want to reduce the waiting time X% they need to hire 1 more person.  Logically This can be done but I need some calculation for this.  A Simulation process could be good for this purpose ?
    2). If we run an experiment for instance with 64 run (2*2*2*2*2*2) and the data that I have , has 1000 datas.  How can I select just 64 datas to run the model ?.  At random Is it O.k ?.  Or perform a Factor analysis ?.
    Thanks so much for your comments.
    Jose Ramon 


    Robert Butler

    1.  If we assume the high and low settings for A,B, and C are
         A – 2, 3
         B – 2, 4
         C – 1, 2
      Then this is the region for the design.  If you ran the DOE and made the various changes in personnel and measured the resulting output (waiting time) for these various combinations and developed a predictive equation for waiting time based on A,B, and C and if you then confirmed the equation by making changes that resulted in waiting times that were as predicted (that is within 2 standard deviations of the prediction where the standard deviation is the RMSE of the predictive equation) then you have all you need to predict what you will get with changes in personnel at A,B, and C.  If you can show a combination that results in a waiting time of 60 seconds then that should be all you need for your presentation to management.
    2. If you run a full factorial DOE – six variables at 2 levels you will have 64 separate combinations.  You say you have “1000 datas” – from this experiment.  What does this mean?
    a) 1000 measurements at each of the 64 combinations?
    b) 1000 measurements across all of the 64 possible combinations?
    or something else.
    If it is 1000 measurements at either a or b then the question is how were they made?  Did you set up one combination of personnel and then take a number of measurements and then convert to another combination and take a bunch more or did you do the near impossible and set up one combination, take a single measurement, and then change the personnel setup and take another?  If you did anything except the last then your DOE measurements are repeat measures and you will have to run the analysis using the methods of repeat measures.
      More to the point, I’ve been trying to understand how you could have equations with so many high level interaction terms that were significant.  However, this would be he case if your method of measurement has been to set up personnel and then take repeated measures on the wait time for some number of minutes or hours or days and then run your analysis as though these measures were truly independent measures of the system. 
      If this is what you have done your computer program is treating the measurement-to-measurement variation within an experimental set up as the true measure of system error.  This error is much smaller than the true system error and the result is that many things will test significant when, in fact, they are not.
      If you have 1000 measurements from the design then the short answer is you would use all of them for the analysis but if they are repeat measures you will have to have a regression package that can handle this kind of data.
       I’m not sure what you mean when you ask:
    “Can  you integrate DEO with F & T-Test?”
       If by DEO you mean DOE then there isn’t anything to integrate – DOE is a method for gathering data, F and t-tests are methods of data analysis.  If you are asking if you can use these tests to analyze the data then the answer is yes, if you want, but it wouldn’t be a terribly efficient use of the data you have nor of the time at your disposal.


    Jose Ramon

    Mr. Butler….thanks a lot for your post.
    It is true what you said.  I have employees in different department and I take measure ( waiting time ) in different days of the week.  I am taking measures in this way.  Every 30 Min….10 times….this mean in one day of 8 hours 160.  The company use, for instance in the department A (1,2).  This mean accourding to my equations that the minimum waiting time that I can manage is 53 sec.  If i want to reduce this time this mean I need somebody else right ?.
    One more point,  If I run an experiment with 32 run and the data that I have is 160 how can I select the data to be tested in the experiment .  I am selecting it at random and sometime when I reduce the model,  the inteactions ( p values ) something is wrong because when I do it interaction P values are not less that 0.05…..and I reduce one and one more time and the result just the main effect are in the output.  This is like :  Y = 53 + 43*A – 4 *B +54*C
    Then I try another data at random at seems to be good.  Why this happen ?. What I did wrong ?.
    About my question of 1000 datas this was just a question.  I do not have 1000 but 160.  But the concept is the same.  I run an experiment with 32 run… random is ok ?.  Or This depend on my experiment run ?  This means is  the experiment run is 32 I have to collect just 32 datas ? Is this good to run a good model ? or 100 at least ?
    Thanks so much.
    One more thing: I did not write this question : “Can  you integrate DEO with F & T-Test?”…………………I do not understand what do you mean ?
    Jose Ramon


    Fake ATI Alert

    Thank You


    Robert Butler

      If you have a single experimental setting (a single experiment from a DOE) and if you take measurements at that setting in the way you described (“I am taking measures in this way.  Every 30 Min….10 times….this mean in one day of 8 hours 160.”) then these measurements are not independent of one another.  You would use all 160 (or whatever number of measures you took) for your analysis, however, this kind of data is called repeat measures and you cannot analyze it using the same methods you would use if the measurements were really independent of one another.
      If you don’t take into account the repeat nature of the data you will go wrong and get exactly what you have described in prior posts – a very complex equation with a large number of significant terms.  This is because your software is assuming the measurements are indeed independent and thus that the difference between each measurement within an experiment is a reasonable estimate of the noise of the system.  Since this noise (error) is much smaller than the real noise of the system your program will identify model terms as being significant when they are not.
      The last comment of my previous post concerning DEO was meant for the other poster to this discussion not you.


    Jose Ramon

    Thanks Mr. Butler for your comments.
    Now the big question is :  How can I perform a good measurement system ?.  Can I take measures , for instance every 30 min and the amount of measure depend on the amount of customers ?.  Is this a good way ?.
    Thanks so much
    Jose Ramon

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