Re: Help with Tricky Designed Experiment

From: Ray Koopman (koopman_at_sfu.ca)
Date: 12/18/04 

Date: 17 Dec 2004 17:25:07 -0800

Paige Miller wrote:
> Here's the situation.
>
> There is a kettle with four positions at the bottom for the fluid to
> drain out of. Into each position, an orifice is placed to control
> the speed at which material drains out. There are four and exactly
> four orifices, each a different size. Kinda like placing 4 pegs into
> four holes.
>
> So the question is: what combination of placing orifices into
> positions produces the fastest (or slowest) drain time.
>
> Now the design gets tricky because I have 4*3*2*1 = 24 possible
> combinations. This isn't a traditional (fractional) factorial,
> because an orifice can only go into one position. In a traditional
> factorial, I can have X1 be set to the low position, AND ALSO X2 can
> be low AND X3 can be low and so on. However, with the orifices, if
> X1 (position 1) has the smallest orifice, then none of the other
> positions can have the smallest orifice; the other three positions
> must have the larger orifices.
>
> Clear?
>
> So, does anyone have any experience with designs like this? Can you
> point me to a reference?
>
> And specifically, can you fractionate this design? If so, how? If
> the level of factors is coded as the diameter of the orifice (i.e.
> continuous variable), I don't think quadratic terms here are
> meaningful, but interaction are -- do you agree? Or should I code
> the orifices as A B C D (categorical/ordinal) without reference to
> the diameter?
>
> --
> Paige Miller
> Eastman Kodak Company
> paige dot miller at kodak dot com
> http://www.kodak.com
>
> "It's nothing until I call it!" -- Bill Klem, NL Umpire
> "When you get the choice to sit it out or dance, I hope you dance"
> -- Lee Ann Womack

In the absence of any theory that would do structure the four positions
in some sense, I see this problem the same way that Bob Wheeler does:
this is a one-way design with 24 levels.

Quantcast