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Screening DOE

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This topic contains 31 replies, has 5 voices, and was last updated by  Robert Butler 12 years, 4 months ago.

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  • #47183

    Jeff
    Participant

    I’m looking to run a screening DOE.  There are 6 factors:
    A is at 2 levels (quantitative)  /  B is at 3 levels (quantitative)
    C is at 3 levels (quantitative)  /  D is of 2 types (qualitative)
    E is at 2 levels (temperature)  /  E is at 2 levels (quantitative)
    For info, “A” is a diameter, “B” is a thickness, “C” is a % swell, “D” is a type of fluid, “E” is temp, and “F” is a size dimension.
    Also – one fluid has a temp. range of 180 – 250 degrees; while the other fluid has a temp. range of 160 – 180 degrees.
    With at least one qualitative factor, I thought a Taguchi L18 was the best choice for a screening DOE, but I am unsure.  Also – how best to handle the temp ranges for the fluids in the DOE? – each fluid can operate over different temp ranges.
    Also – how many replications are needed?  My understanding is that the # of replications are to be at least 4.
    All responses would be most appreciated.  Thank you.

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    #157024

    Chris Seider
    Participant

    Just do a fractional factorial with all factors at 2 levels only.  That can be done in 32 runs…..assuming you have set the levels far enough, this should give you enough info to screen out those less important….Remember you said you want a screening experiment.

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    #157027

    Robert Butler
    Participant

      It would appear your temperature and your fluids are completely confounded.  You say you have one fluid with a range of 160-180 and the other with a range of 180-250.  If this is the case then 180 is the only temperature where you could run your process and treat the fluid type as a variable “independent” of temperature.  Under these circumstances temperature would not be a variable. Thus, as described,  you have 5 variables – A, B, C, D, and F.  (There are, of course other possibilities – two small designs one for each fluid and each design over a different temperature range).
      As was noted, you said you were interested in running a screening design which means minimum effort for maximum information. I’d recommend a near saturated design – 5 variables in 8 experiments – toss in one or two replicates (this is replicates of a single experiment not a complete replication of the entire design), and your total effort would be 9-10 experiments.  If you really want to check out B at 3 levels you could use D-optimal methods to augment the 8 point design with a couple of experiments to permit this. 

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    #157028

    Jeff
    Participant

    I have a suggestion:
    how about a mixed level Taguchi L36 (2**4  3**2)??
    L36(2**4 3**2)
    Factors: 6
    Runs: 36
    Columns of L36(2**11 3**12) Array
    1 2 3 4 12 13

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    #157122

    Jeff
    Participant

    Sorry – I initially received bad information.  It turns out that the temp. ranges I specified in my earlier note were incorrect.  The correct temp.’s to consider are 180 and 250 (and both fluids are to be evaluated at both temp.’s).
    In actual usage, the temp. will not be a controllable feature (it is whatever the temp. is below the surface, down a few thousand feet).  So it’s a noise factor.  Would this then dictate a Taguchi DOE with temp. as a noise factor?  Or would another DOE be better? 
    Also – if the Taguchi is the best choice, how are noise factors input in software (say, Minitab).  Software seems to treat controllable factors and noise factors similarly.
    I plan on entering some center points to try and detect curvature on 2 factors, but plan on using 2 levels for the other factors of this screening DOE.  Certainly want to get max info from min effort.
    Thanks for your input!

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    #157123

    Jeff
    Participant

    Just wanted to add – this DOE is constrained by being able to have only approx. 20 runs (so replication is not an option unless a small DOE was done – say, with 10 runs or less).

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    #157124

    Robert Butler
    Participant

      Taguchi noise factors are factors you don’t want to control when running your process but which, during the course of the Taguchi experiment, you will have to control in order to use them as variables in a Taguchi design. The post below has more on this subject.
    https://www.isixsigma.com/forum/showmessage.asp?messageID=108236
      As described your temperature cannot be controlled in any way therefore temperature is noise in the statistical sense, it cannot be incorporated into the design, and you will have to randomize your experiments to make sure temperature is not confounded with the variables of interest.  Given this and the fact that you are also constrained with respect to runs I’ll stand by my initial recommendation with respect to design construction. 
      If you want to try what I recommended in my previous post and if you want to investigate B at 3 levels and do not have the software necessary to build an augmented design let me know and I’ll build it for you.

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    #157136

    Jeff
    Participant

    Robert,
    Thanks for your feedback.  I would like to see your recommended DOE setup.  Please note that it would be best if I could investigate factors “B” and “C” at 3 levels.
    If you could let me know what design you recommend and how you build it, I’d appreciate it very much.

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    #157137

    Jeff
    Participant

    Just one more short note – with runs limited at ~20, hopefully some replication can be done.

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    #157141

    Robert Butler
    Participant

    The basic 12 point design is as follows:
            A        D       F        B        C
    1    1     1    -1    -1    -1
    2    1    -1     1    -1    -1
    3   -1    -1    -1     1    -1
    4   -1     1     1     1    -1
    5   -1     1    -1    -1     1
    6   -1    -1     1    -1     1
    7    1    -1    -1     1     1
    8    1     1     1     1     1
    9    1     1     1     0     0
    10  -1    -1    -1     0     1
    11  -1    -1    -1     1     0
    12  -1    -1     1    -1     0
      It was generated by building a saturated 8 point 2 level design (the first 8 points) where the variables are A, D, F.
      B is confounded with the DF interaction and C is confounded with the ADF interaction.  Augmentation was performed using a D-optimal design package and limiting the augmentation to 4 additional runs.  The VIF’s range from 1.08 to 1.18 and the condition indexes range from 1 to 5.9.  The usual upper bound for both of these statistics is 10.
      The design will permit an investigation of the effects of A,B,C,D, and F as well as the curvilinear effects of B and C.  With a limit of 20 you can choose up to 8 of the points for replication.

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    #157145

    Jeff
    Participant

    Thanks very much, Robert!
    I will take a good look at this setup

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    #157147

    BC
    Participant

    Hi Robert,
    Your posts indicate that you’re pretty knowledgable in DOE.  What is your opinion regarding the use of Taguchi L12 or other partially-confounded designs for screening?  This is an approach that Air Academy teaches and it seems reasonable on the face of it.
    Thanks,
    BC

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    #157148

    Robert Butler
    Participant

     Saturated designs, of which the L12 is but one example, are very useful for screening and I’ve used them countless times.  Obviously they ignore interactions and curvilinear effects but they allow a very quick check of a laundry list of potentially important variables with a minimum expenditure of time and money.
      If all of the variables are continuous the only thing I will add to a saturated design will be a center point and its replicate.  The addition of these two experiments buys me information about the existence of curvature in the design space (although I won’t know which variable(s) is (are) the cause) as well as giving me an estimate of pure error.

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    #157149

    BC
    Participant

    Thanks Robert.  I appreciate your comments.

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    #157154

    Jeff
    Participant

    Robert,
    I see how you generated your design and how you generated additional columns for factors B and C, but I’m hung up on how Minitab adds in the additional 4 rows.
    Minitab has an augmentation function with the D-optimal design, but I’m receiving an error message that “the number of optimal points is smaller than number of terms”.  Is Minitab the software that you’re using?; is there a key step that is missing?

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    #157156

    Robert Butler
    Participant

    I use Statistica for generating my designs.  I don’t know Minitab but it sounds like you haven’t given the program the candidate points from which to choose.  In Statistica you give it all of the possible combinations (72) – force it to accept the 8 corresponding to the near saturated design, and then tell it how many more experiments you want to add to the design.  I suspect Minitab works in much the same way.
      I told my machine to give me 4 more experiments in order to provide information on the squared terms.  After it generated the design I tested it to make sure the VIF’s and the condition indexes were within limits.

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    #157157

    Jeff
    Participant

    What are the 72 possible combinations that you mentioned?

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    #157158

    Robert Butler
    Participant

    all of the possible experimental combinations
    -1 -1 -1 -1 -1
     1 -1 -1 -1 -1
    etc.

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    #157162

    CT
    Participant

    Jeff
    I almost hate to say this because I think MTB has a very poor help section, but in this case setting up your DOE for the combinations you want is pretty clear under the Help Menu.
    Good Luck
    CT

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    #157166

    Jeff
    Participant

    CT – I agree that Minitab has pretty thorough help section on augmenting a DOE with a D-optimal design, but I keep getting this error.

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    #157170

    Jeff
    Participant

    Minitab is not so friendly in this task, but I augmented Robert’s saturated 8 point design and got 12 points (the 8 original and 4 additional; the 4 additional points still satisfying the confounding requirements of the first 8 points).
    My question is: these 4 addional points are not created by Minitab to be center points (at least for factors B and C).  Can this be done (other than manually)??  Or does one need to manually enter “0”‘s??

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    #157171

    Robert Butler
    Participant

     I’m not quite sure what you mean.  The selections of -1’s , 0’s, and 1’s will come from the 72 choices you gave the machine. The fact that the D-optimal routine didn’t happen to choose any of the experiments with a B, C center is interesting but not particularly surprising.  Optimization routines focus on their specific criteria used for augmenting and that criteria may or may not be such that the best choice for an additional design point is a center.  If you want to have a center for B and C you can certainly add one of the B,C  center experiments (see below) to you list of 12.  Since D is a categorical variable (either one kind of fluid or another) you might want to choose 2 center points on B and C just so you have that center run at both of the D conditions.  This isn’t necessary but there are some people who feel more comfortable if they know they have done this.  If you do this the final design will be 14 experiments – add a couple of replicates and you will have 16 which is still below your maximum of 20.
    -1     -1     -1     0      0
     1     -1     -1     0      0
    -1      1     -1     0      0
     1      1      -1    0      0
    -1     -1      1     0      0
     1     -1      1     0      0
    -1      1      1     0      0
     1       1     1     0      0

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    #157174

    CT
    Participant

    Jeff
    There is a way to do it. If you have the time, give me a little while and I will work on. I think I know what you are trying to achieve and how to get there. A funtion in the setup is not turned on or not added in the initial setup and I need to read up on before I make any brash statements.
    CT

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    #157189

    Jeff
    Participant

    CT & Robert,
    I should have a decent idea of how to work the D-optimal setup in Minitab.  One thing I did wrong was to not set up the initial 72 point General Linear Model initially (I just set up the saturated L8, as opposed to initially creating the GLM and then applying the D-optimal routine).
    That said, Minitab still did not create any center points for factors “B” and “C”, but, as Robert said, those can be added in.
    A question I still have is that Minitab requires that the # of defined terms (e.g., linear / interaction / quadratics / etc.) be less than either the # of candidate points or the # of final optimal points.  As I was aiming for a 8 initial points, I could only use the 5 linear terms / then, with aiming at 12 final optimal points, I still had to use only these 5 linear terms (as the total of linear and interaction terms was 13).
    I appreciate all your help.  I’m really driving to get this D-optimal routing down because it’s so useful.  So many situations come up in which time or $ is a contraint and the # of experimental runs is limited.  It’s great to have the flexibility to create an array which is optimized within ones constraints.

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    #157190

    CT
    Participant

    Jeff,
    You must define that B,C are center points by selecting General Full Factorial, be sure that under LOW/HIGH the Coded button is selected. This should give you the design you are looking for with
    -1

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    #157191

    CT
    Participant

    Jeff,
    You must define that B,C are center points by selecting General Full Factorial, be sure that under LOW/HIGH the Coded button is selected. This should give you the design you are looking for with
    -1 

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    #157192

    CT
    Participant

    Jeff,
    You must define that B,C are center points by selecting General Full Factorial, be sure that under LOW/HIGH the Coded button is selected. This should give you the design you are looking for with
    -1  

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    #157193

    CT
    Participant

    Note to self: DONT HIT FREAKING TAB:
    Jeff
    You must define that B,C are center points by selecting General Full Factorial, be sure that under LOW/HIGH the Coded button is selected. This should give you the design you are looking for with
    -1      0       1      layout
    Hope this helps
    CT

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    #157195

    Robert Butler
    Participant

      I don’t think you are specifying the model correctly.  With the 8 point near saturated design you can look at A,D,F, B, and C. (you can also look at the AD and AF interactions).  To get the curvilinear effects of B and C you would tell the machine to look at A,D,F, B, C, B*B, and C*C and tell it to force in the original 8 point design. 
      It sounds like you are trying to force in all of the two way interactions as well as all of the main effects (15 terms total).  If you add the two curvilinear terms you are now up to 17. You can, in fact, build a D-Optimal from scratch (no augmentation here) with 18 experiments and leave room for 2 replicates, however, when you squeeze things this tightly you need to have some way to check the design to make sure that the generated design is acceptable.  I did a quick check with several iterations of the 18 point design (in order to leave room for two replicates and still have the total = 20) and while the VIF’s are within limits the condition indices are not – specifically I couldn’t get the machine to build a design that gave condition indices that were less than 10 for both of the curvilinear effects. 
     

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    #157198

    Jeff
    Participant

    Robert,
    I followed your last note and got “B” and “C” center point runs for either 8 run or 12 run DOE’s.  Thank you.
    One other question:   why would one include the B*B and C*C quadratic terms to examine curvature for B and C??

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    #157199

    Jeff
    Participant

    Thanks CT.  Generating the full GLM initially was the way to go.

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    #157201

    Robert Butler
    Participant

      If you want to look for curvature in B and C using one of the optimal algorithms you have to indicate you want to look at more than linear effects.  The way to do this is to ask for quadratic effects – the square of B and C.  Since it takes a minimum of 3 points to determine a curve this will force the machine to include experimental combinations that look at the three levels of B and C ( -1, 0, and 1).  If you don’t do this it is very unlikely that the optimal package will include design points containing a 0 level for B or C.

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