I am trying to conduct a DOE. I have 4 factors and each has 5 levels. When I tried to get the experiment order setups using Minitab I got the following:

Multilevel Factorial Design

Factors: 4 Replicates: 1
Base runs: 625 Total runs: 625
Base blocks: 1 Total blocks: 1

Number of levels: 5, 5, 5, 5


Minitab list 625 runs for these factors with 5 levels. I am trying to reduce the number of runs and see if I can get a DOE. Also I wanted to have some replicates for the run. But if I increase the replicates, the number of runs also increases.

What design should I be using? Can somebody help me on this? Your help in this regard is greatly appreciated.

Thanks.

Are the 4 factors variables (that you can set to various levels along a continuous scale, like temperature) or are they attributes (non-numeric values, like five different sources for a raw material)?

If the factors are variables, then a CCD (central composite design) would work well since it naturally has 5 levels. This would require about 30 trials

If the factors are attributes, then a Taguchi design could work. I know there is a "L25" design with 25 trials for up to 6 factors at 5 levels. Since you only have 4 factors, you can just ignore the last two factors in the design.


Tim F

Thanks for your reply.
The factors are variables, so I am going to use CCD. But when I look at the inputs for CCD, it has only high and low values for factors. So should I be using the center points as 3 or leave it to default.
Once again thanks a lot for your help.

Minitab's use of "high" and "low" is a little confusing. The high and low values are for the "cube" points. The default value for the "axial" points is greater than the "high" and "low" !

For 4 factors, the "axial" points are twice as far from the center as the "high" and low". For example, if you temperature was a variable and you set the high = 100 and low = 60, then then the center point would be 80 ( the average of 60 and 100). Most of the trials would use temperature of 60, 80, and 100. but a few (one each, it looks like) would be 20 farther out - at 40 and 120.

A little algebra suggests that to get the actual max and min you want, you should set the high to (3/4 max +1/4 min) and the low to (1/4 max + 3/4 min). In the example above, max = 120, and min = 40, so

high = (3/4 * 120 + 1/4 *40) = 90+10 = 100
low = (1/4 *120 + 3/4 *40) = 30 + 30 = 60

which is indeed is what we had, so I trust the algebra!



Tim

P.S. the axial points are different amounts out depending on how many factors you have, so the above equations don't necessarily work for other numbers of factors.

Thanks for the great description on the CCD design and easy way to set high/low values in minitab.