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Hello Everyone,

Thought I would reach out to the SE community for an answer to my customers question below:

Can you provide me some insight  on situations where a fractional factorial design would be preferable to a DSD?

Thanks,

--Mary

Re: Definitive Screening Design (DSD) or Fractional Factorial

In regards to 1., I should mention that covering arrays aren't intended to use a linear model, but for a deterministic (typically binomial) response. This is especially true since they'll typically be supersaturated even in regards to a main effects model. That said, they do have promising projection properties that could be useful as a supersaturated design.

And I've seen the same thing with your points in 2. Those that have grown accustomed to regular fractional factorial designs may be scared off by the partial aliasing in the two-factor interactions from a DSD, and would rather have the complete confounding in a resolution IV design that they'll try to separate later. Even if you weren't interested in the quadratic terms (or had 2-level categorical factors), I'd still probably go with an alias optimal design, but I'm a bit biased in my opinion

As mentioned above, if you had the resources to the run the design, there certainly may be preferences given to a resolution V design if wanting to estimate all the interactions, or an RSM design if wanting all those effects.

Cheers,

Ryan

Re: Definitive Screening Design (DSD) or Fractional Factorial

OK...I slept on Mary's question and came up with a few other thoughts:

1. What about a situation where a covering array might be an appropriate design approach? Isn't a covering array a kind of fractionated design in that we're purposely choosing treatment combinations to estimate specific effects...and not all possible effects. Which I guess I'd term ANY design that does not allow independent estimation of all possible effects a form of a 'fractional factorial design'?

2. Then there's the Taguchi 3**(k-p) level design afficianados. Before everyone thinks I've lost my mind here...please read on. These people INSIST on forcing their designs into his L(number of runs) construct. In this scenario design selection is influenced more by personal preferences and biases of the people involved in planning the experiment rather than statistical/modeling efficiency, power, estimability, etc. Often during my career I had to bite my tongue with a person who was relatively new to DOE and just getting them to run ANY designed experiment (even if there were other more efficient options ) was a major breakthrough. So sometimes we had to go along to get along and we'd go down this path and I'd hope that for future work we can open their eyes to other more efficient design families and paths.

Re: Definitive Screening Design (DSD) or Fractional Factorial

Mary,

The question is specifically directed at the comparison of Fractional Factorials versus DSD's

One scenario would be a small number of factors (<6) to examine (although I would challenge any experimenter to consider more factors).

A second scenario might be where the effect sparsity turns out not to be in one's favor and a RES V would be less challenging to analyze.

Having said that, the added advantage of getting a sense of the polynomial active effects greatly outweighs the modeling challenges since augmentation and verification are your friend.

Outside the realm of Fractional Factorial comparisons dealing with multi-level categorical, split-plot scenarios and constraints make Custom DOE the flexibility champion.

Re: Definitive Screening Design (DSD) or Fractional Factorial

I think I saw a video somewhere from Stu Hunter where the interviewer (I think our own Anne Milley?) asked Stu Hunter what he thought about DSDs. I think Stu's response was something like, "I think they essentially render 2**(k-p) RES III and IV designs obsolete." Pretty high praise for DSD's compared to these stock in trade historical screening designs.

I guess I could make an argument for some RES V designs, that I wanted a response surface model (hence I've got to run say a CCD attached to my RES V 2**(k-p), or what we used to call a Frankensteen design?) and I bludgeon the design to death with sample size to raise power...but this gets off into the land of unlimited budgets. Quite frankly, for the classic true SCREENING of key factors problem, where economy of experimental conduct is paramount, hence I'm entertaining running 2**(k-p) RES III or IV designs...I'm hard pressed to come up with a reason to run one of these 'fractional factorial designs' compared to a DSD. I'm with Stu Hunter...I wish DSDs were invented during my time at Kodak. I'd have never looked back I suspect...