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I am looking for help to set up Taguchi DOE for welding process. We identified total 15 factors (3 factors with 5 levels, 8 factors with 3 levels and 4 factors with 2 levels). I will appreciate if anyone can help to set up the experiment or point to the right direction.

Consider a factorial design and reduce the number of experimental runs required to find a gross direction first for your inputs since you’ll use 2 levels only in a factorial design.

If you have run your brainstorming session and if you have put your old production data through a wringer looking for possible associations between input and output and the end result is your list of 15 variables then you will want to run a preliminary screen design to look for significance of simple main effects with the hope that an effort of this type will reduce your list of candidate variables so that you can set up a more complex design to investigate the reduced list.

You didn’t say what kinds of variables (factors) you have – are they all continuous, a mixture of continuous and categorical, or all categorical.

If they are all continuous you can run a two level 16 point saturated design with two replications on the center and use the results from that 18 point run to look for initial trends and reduce the number of variables for a follow up analysis. If the factors are a mix of continuous and categorical or all categorical then you will need a different design matrix.

Thanks Robert. We had a brainstorming session, we developed mixed continuous and categorical factors for the experiment. I need a mixed design Taguchi experiemnt. Any help?

I don’t think you need a mixed design Taguchi experiment. What you need is a basic fractionated design which takes into account categorical and continuous variables. If you can post your matrix of variables in the form of

Variable 1: Continuous – 3 levels

Variable 2: Categorical – 2 types

etc.Perhaps I or someone else can offer a design for your consideration.

Anil SachdevI think it will be good to screening experiment such as fractional factorial or Plakett-Burman and reduce the variables to a manageable number (<5). Then go for Taguchi design. Taguchi design with 15 factors is not a good idea practically.

Thanks Robert, Manee and Anil for your input. Following are the factors (15) and Levels (5, 4,3). My objective is to minize experimental cost. We are estimating to complete this experiment will cost around 300K. Any one can help me to design this experiment. I apprecite any help to set up the DOE.

Factors Levels Level 1 Level 2 Level 3 Level 4 Level 5 Units

1 Wire Feed Speed 5 3.5 4.0 4.5 5.0 5.5 m/min

2 Amps 5 115 125 135 145 155 A

3 Volts 5 15 16 17 18 19 V

4 Wire 3 L-56 70S-G K Nova Ni wire

5 Gas 3 80/20 75/25 50/50 Argon/CO2

6 Flow Rate 3 25 28 31 L/min

7 Oscillation Speed 3 50 100 150 cm/min

8 Oscillation Width 3 0.5 1.3 2.0 mm

9 Oscillation Dwell 3 0.1 0.2 0.3 s

10 Travel Speed 3 15.0 25.0 35.0 cm/min

11 Bevel Land Thickness 3 1.2 1.5 1.8 mm

12 Bevel Land Extension 3 -0.2 0.0 0.2 mm

13 Material Source 2 Sumitomo Tenaris pipe source

14 Wall Thickness 2 0.750 1.250 in

15 Outer Diameter 2 6.625 10.75 inThanks for the matrix. It appears that you have two categorical variables (wire type and material source) but maybe it is just one. The issue is/are the differences in wire type? Is there any chance these could be ranked on the basis of something like alloy/material composition, hardness,etc. If you can do this then wire could be treated as continuous.

If you can treat wire as continuous you could run a near saturated design of 14 variables in 16 experiments. If each design included two “pseudo” center points (middle levels for every continuous 3 and 5 level variable and a random choice of a high or low value for wall thickness and outer diameter)then you would have 18 points per material source for a total of 36 experiments.

If, on the other hand, wire is a type variable and you cannot find some underlying continuous variable to characterize the types then you will have to run the 18 point design 6 time for a total of 108 experiments.

The 18 point design will allow you to test for the significance of the simple linear effects of the 14 continuous variables and test for the presence of curvilinear behavior (if the curvature is significant you won’t be able to tell which variable(s) is/are responsible but you will at least know that the effect is present and significant)

If you are faced with having to run a design for each of the 6 combinations of the type variables you should go back to your team and ask for opinions with respect to which of the 6 combinations of wire type and material source are viewed as the “best” and which are viewed as the “worst” and then run the first two groups of 18 experiments with these two combinations of wire type and material source and analyze their results before moving forward.

One assumption with respect to the above comments – it is assumed that you can vary all 15 variables independently of one another. If this isn’t the case then you will have to tell us which variables and at what levels are restricted – that is which of the variables and their levels must change at the same time.

If you can answer these questions I suspect we can build a design which will meet your requirements.

Thanks Robert. I appreciate your prompt response. I will send your question to our welding engineer. I will get back with you soon. Regards

@ahsanhuq – you are probably looking at amps and volts as discrete settings as they have distinct positions on the welding machine. This would be improper (and as Robert has identified, these are really continuous). I agree with Robert that you can probably also characterize the weld wire as continuous if you can find the critical parameter that is achieved by the different wires (which may even point you to a different wire in the end if that characteristic is significant and not optimized by these two choices!).

It is always better to find a way to characterize your variables to be continuous. This may take work and ingenuity to find the characteristic which can be measured on a continuous scale, but in the end, doing so will provide much better results.

After the optimization is done, if you find that an input must be set at a discrete setting, you can use your optimization equation to estimate the difference from the ideal by using the closest discrete levels. You can then decide whether this is sufficiently good enough, or if it justifies the investment in a capability to make that input variable more suitable to the ideal level – perhaps purchasing a new machine or re-working the controls to allow more fidelity in the settings.Thanks Robert and MBBinWI for your input. Following is our welding expert comments on your suggestion or question (Q: from you ans ANS: from our expert). Any thought??

Q: Thanks for the matrix. It appears that you have two categorical variables (wire type and material source) but maybe it is just one. The issue is/are the differences in wire type? Is there any chance these could be ranked on the basis of something like alloy/material composition, hardness,etc. If you can do this then wire could be treated as continuous.

ANS: No, wire type cannot be ranked on alloy/material composition or mechanical properties. We have a narrow scope of acceptable properties that limits the available wire products for use. We are not in a position to formulate our own wire, so we cannot vary composition or mechanical properties beyond the choices we have from vendors. These should be considered discrete at this time.

Q: If you can treat wire as continuous you could run a near saturated design of 14 variables in 16 experiments. If each design included two pseudo center points (middle levels for every continuous 3 and 5 level variable and a random choice of a high or low value for wall thickness and outer diameter)then you would have 18 points per material source for a total of 36 experiments.

If, on the other hand, wire is a type variable and you cannot find some underlying continuous variable to characterize the types then you will have to run the 18 point design 6 time for a total of 108 experiments.ANS: The 18 point design will allow you to test for the significance of the simple linear effects of the 14 continuous variables and test for the presence of curvilinear behavior (if the curvature is significant you wont be able to tell which variable(s) is/are responsible but you will at least know that the effect is present and significant)

This concerns me because I already am aware that many of the responses will not be a linear affect…

Q: If you are faced with having to run a design for each of the 6 combinations of the type variables you should go back to your team and ask for opinions with respect to which of the 6 combinations of wire type and material source are viewed as the best and which are viewed as the worst and then run the first two groups of 18 experiments with these two combinations of wire type and material source and analyze their results before moving forward.

One assumption with respect to the above comments it is assumed that you can vary all 15 variables independently of one another. If this isnt the case then you will have to tell us which variables and at what levels are restricted that is which of the variables and their levels must change at the same time.ANS: Pipe availability is probably the only dependent part (i.e. maybe only certain suppliers with certain sizes available)

Q: If you can answer these questions I suspect we can build a design which will meet your requirements.

you are probably looking at amps and volts as discrete settings as they have distinct positions on the welding machine. This would be improper (and as Robert has identified, these are really continuous). I agree with Robert that you can probably also characterize the weld wire as continuous if you can find the critical parameter that is achieved by the different wires (which may even point you to a different wire in the end if that characteristic is significant and not optimized by these two choices!).

ANS: The following weld parameters should be considered continuous:

Wire Feed Speed

Amps

Volts

Gas Flow Rate

Oscillation speed

Oscillation width (restricted by bevel width)

Oscillation dwell time

Travel SpeedParameters could be either (we have discrete settings, but could do custom adjustment to cover continuous settings):

Bevel land thickness

Bevel land extension

Wall Thickness (we can counterbore to smaller wall thicknesses for a continuous setting)The following parameters are discrete:

Pipe Material (discrete availability)

Outer Diameter (generally set by API standards 4.500, 5.5625, 6.625, 8.625, 10.75, 12.75, 14.000, 16.000,… etc)

Gas (can be continuous; however, it is more reliable to stick with standard balances 50/50, 75/25, 80/20, 90/10,…etc)

Welding Filler metal/wire (there are only certain types available that meet our requirements, we can increase the test scope…but I am not sure we can do anything on a continuous scale)What we have is a classic case of concluding things are discrete – that is categorical – when in fact they are continuous (my engineers do this all the time so this view is quite common). I realize the various gas mixes, diameters, bevel land thickness, etc. are fixed in the sense that suppliers will only provide you with certain mixes, diameters, etc. However, in principle, they could be made to be anything you or the suppliers wanted to make them. Under these circumstances the practice is to treat variables of this type as continuous and analyze them in that manner.

It was for the above reason I asked about the wire – it can’t be changed but it can be characterized by important composition properties and thus it could be treated as continuous.

What this ultimately translates into is a drastic reduction in the number of needed experiments.

I want to mull over your post some more before adding anything else.

I’ve been silent during the great help from my colleagues but don’t attempt to fully understand your 15 factors and interactions in your first DOE. Consider a fractional factorial design as we’ve hinted earlier. Not all factors will be statistically and practically important.

I still think you should do a fractional factorial design with 2 levels. I am inclined to not worry about running a center point in the screening design. This screening design can be done with both categorical and continuous variables.

Thanks Robert and Chris. I really apreciate your input. Can we trean all the afctors are continuous and design the experiment? One of the objective is to reduce # of experiment.

@rbutler earlier said you can check out with a screening design of 16 runs for 15 factors. You won’t have definitive understanding of effects and interactions but you’ll know which are so small practically and/or statistically that you can then run a more descriptive DOE with fewer factors afterwards. We’re advocating a simple 2k factorial design instead of Taguchi because of our preference.

Robert is encouraging you to treat them as continuous which is always nicer but you’ll find out significance (screen for importance) even if you treat some as discrete. Again, I would advise against using a center point in the 2**(15-11) design which will have 16 experimental runs with no replicates since you’re only screening but it’s not WRONG to use a center point–especially if you can somehow run in the middle of all your variables if they are continuous.

You may say hey the 3 positions for amps are de facto discrete but if you treat as continuous, the middle position can be your center point. Robert’s advice gives you an idea of repeatability (process variability) when you run center points but I don’t usually do that if screening–especially for so many factors.

I’m not speaking for Robert but we have a similar perspective typically. :)

Based on your last post it looks like we have 13 variables we can treat as continuous

Wire Feed Speed

Amps

Volts

Gas Flow Rate

Oscillation speed

Oscillation width (restricted by bevel width)

Oscillation dwell time

Travel SpeedFor the following use whatever is available and pick a small and a large value from these or in the case of the gas two standard ratios.

Bevel land thickness

Bevel land extension

Wall Thickness

Pipe Material

GasThe remaining issue is that of supplier and wire type. It sounds like the supplier issue is that of provider of pipe. If, from the standard sizes, you can pick a small and a large value that both suppliers offer then you can randomize the assignment of the pipe diameters to the design points which will effectively randomize across supplier and thus shift any effect supplier difference might have into the error term. In other words 8 of the design points will have small pipe and 8 will have large get 4 samples of each from each of the two suppliers and randomize the assignments of pipe to the associated design points.

The design is a maximally unconfounded Resolution III for 13 factors in 16 experiments. I would recommend replicating either a random choice of two of the 16 experiments or using a pseudo-center point as mentioned earlier and running that point twice. The attached design has a random run order and should be run in the order listed. You will want to add the replicates at random points during the run and, since there are two wire types which cannot be treated as continuous you will need to run this design twice for a total of 36 experiments.

To the issue of known curvilinear responses and the interest in running more than two levels: Chris has already commented on this and I would add the following: Most curvilinear responses follow an asymptotic curve of some kind. As a result you will have a response in the form of low, medium, high or high, medium, low where the medium point is not on a straight line between the other two values. If the response is in this form and if the trend is significant that significance will be detected with either a simple linear fit or with a curvilinear (typically quadratic) fit. The only type of curvature that a linear fit will miss is the form of low(1), high, low(2) where the slope of a straight line between low(1) and low(2) is small (think of a parabolic curve) . This kind of a response trend is not common. In my experience it is most likely to happen when you have crossed some unknown phase boundary within the process (e.g. you are making mixtures where a rubber compound is the additive and you have a matrix of plastic and rubber and the proportions of the two shift so that it becomes a matrix of plastic in rubber instead of rubber in plastic).

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@ahsanhuq – you can always treat a variable as continuous for the DOE using a “low” and “high” setting. You will want to examine the response to see if this is sensitive and if it has interactions. If not (often the case) then after optimizing, you will need to pick either the “low” or “high” setting for the parameter (and re-run the resulting optimization equation to see what the expected output should be).

As Robert said, just because something normally is found in a discrete format doesn’t mean that for the experiment you need to treat it as discrete. And if you find that it is sensitive and critical enough, you may find that getting a non-standard item is worth the effort/cost.Hi Robert; Do you mind to show me how to put together the experiment based on your assumption? Apprecite for your help.

The assumptions were two levels for each of the variables that could be treated as continuous. The method for design generation was the experimental design package in Statistica and all I specified was the fact of 13 variables at two levels and a request for a near saturated design of 16 points. If you have Minitab or one of the other statistics packages with a design construction capability I’m sure the commands for design generation will be similar.

In the event that you don’t have any access to a design package you can generate a very similar design by writing out the full matrix for a 2**4 experimental design and, starting with the ABCD interaction work your way backwards through the 3 way and two way interactions (in Yates order) and assign variables 5-13 to these terms. (That is, variable 5 = ABCD, variable 6 = ABC, variable 7 = ABD, etc.) I don’t think the design will be an exact match for the one I posted but it will be close and, if you need something more than a listing from a poster on a forum for purposes of design justification, this method of variable assignment is as old as the concept of fractional factorial designs itself.

i want taguchi to determine the most important factor affecting my nanoparticle size. i have 3 factors, two of them with 7 level and one with 6 level. my factors are ph, time and concentration of HNo3. i can not find a design in minitab which has this number of level. can you help me in this regards?

You won’t find any design with that many variables levels and you are wasting your time trying to take that many levels into account. Consider what 7 levels implies: the underlying response is septic – a 7th order polynomial. I’m not aware of any physical response that requires that degree of polynomial in order to describe its behavior.

If you have 3 factors the quickest check would be a simple 2 level factorial design with a couple of center points for a total of 10 experimental runs. That design would cover all of your main effect, all two way and the three way interaction and it would give you a test for the existence of curvilinear behavior. If you want to cover curvilinear behavior and all of the two way interactions then you could set up a D-optimal design. You could do this in 15 runs, add two center points for replication for a total of 17 runs and have it all. The D-optimal has VIF’s and condition indices that are within limits. Below is such a design – it looks ok in the typing window but I’m not sure how this will translate to the post. The columns may not line up straight.

EXP x1 x2 x3

1 1 -1 0

2 1 0 -1

3 1 -1 -1

4 -1 1 1

5 0 1 0

6 1 1 1

7 0 -1 -1

8 0 0 1

9 -1 0 0

10 -1 1 -1

11 1 1 -1

12 -1 -1 -1

13 1 -1 1

14 -1 -1 1

15 -1 1 1

16 0 0 0

17 0 0 0I am looking for help to design Taguchi Design for mixing parameters. I have 3 different mixer type and their speed and time as factors. After set up the design like 3 factors 3 levels, I realized that speed and time factors are dependent. For example, 1st factor: extruder base mixer, speed; 100 200 300 rpm and time; 5 10 15 min, 2nd factor V blender, speed 50 100 150 and time 1 5 30 min. Is it possible to create dependent variables for Taguchi Design? I found similar information in the “Properties of the Taguchi Capability Index for Markov Dependent Quality Characteristics” but I do not fully understand.

From your description it is not clear that time and speed are coupled. Do you actually mean this – that is – is there something that physically prohibits your changing speed and time independent of one another? The reason for asking is because I’ve worked with extruders for plastic pellet manufacture in the past and these variables were not coupled. What we did have was a series of “settings” where certain factor combinations were understood to be optimal and the reason we ran the design was to check the validity of these understandings.

If they are indeed coupled and cannot be changed independently then you will be faced with a single time/speed variable and will have to run the analysis with the two confounded.Thank you, Robert, it is a very good point. What I try to understand from my set up is that time and speed effect on the product quality. Depend on my product, there is a speed limitation. I couldnt go over the certain speed. Since some of the mixer types work faster than the others I couldnt also set up the same speed level. For example, for the impeller mixer, my min speed is 60 rpm while the other type mixer starts from 1350 rpm. So, the levels do not match. They are depended on the mixer type. If I put the low/middle/high instead of the numbers for level, then I can perform L9 array design. For this case, lets say the low level will be 60 rpm for the impeller and 1350 rpm for V-blender.

Ok, then the experimental design will have to be a separate one for each mixer type. This means you set up a generic design as you have already noted and plug in different ranges of time and speed values for each machine. By the way, if this is a straight up 3 level design for two variables and there isn’t anything else you are interested in considering then a 3**2 should do it for you.

On the other hand, if you have what the Taguchi crowd calls a noise variable then I would recommend you re-think your design choice and build a desigh which includes the extra “noise” variable(s) as regular variables in the design and use Box-Meyer methods to assess the impact of changes in variables on the output variability.

Thank you, Robert! I will definitely check the Box-Meyer methods and will consider your suggestion.

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