The situation you mention is being observed because your response vector Y has projection on a large no. of 1D, mutually orthogonal Subspaces each associated with a main effect or multifactor interaction effect you mentioned above, In such situation you can achieve variable screening in the following way:

Pre decide a threshold level of variation about mean, e.g 80 to 90% of your total variation. Now order the sum of squares associated with each effect from largest to smallest, including the non significant terms as well, now retain only those effects, main and interaction type that account for your "desired level" of variation contribution, by playing around with this threshold a little you might be able to weed out some borderline statistically significant terms yet retaining a significant portion of total variation in your truncated model.

An alternative is model respecification, try to think about some alternate set of input variables, functionally related to A, B,C,D factors and try DOE with these transformed variables and response Y, this might give you a more uneven variation partitioning than the case of your previous set of variables chosen.

The situation you are facing is not uncommon or erroneous, there was a paper I read long ago where the author has presented a set of real world examples of such cases where principles of confounding break down and where interaction effects turn out to be significant but main effects not and so on, Unfortunately I cannot recollect the title of the paper or author name at this moment...but it was a science direct journal...I will provide you the details about this paper after some days.

You can also contact the experts team of Design Expert with this issue, also Design Expert website contain a large collection of material covering several aspects of DOE , you can get some insights into your problem from those material also.

Without more information there could be a few explanations.

Most people don't get lucky enough to find significant three ways as Dawes and Corrigan found years ago that main effects and two ways will account for most of the variation (upwards of 90% perhaps but don't quote me in that figure as it's been a while since reading).

The ability to detect significant effects does depend on sample size. So if you are using repeated observations you may want to adjust that standard error in the denominator of your t stat using robust SEs.

Of course this assumes you actually had a design that can detect these effects. If you used a fractional factorial then being able to detect these three ways may or may not be possible depending on what their confounded with.

As always a soon as you have significant two or three ways you can no longer look at the main effects in isolation to make your interpretation. I find the best way is to plot these holding one factor level constant as a series with the other two varying.

I hope that's given you a few ideas and be interested in your response to see if any of that is on or missing the mark.

Paul b

It could be due to using a large sample size which would improve your ability to detect significant effects relative to a smaller sample size. Out of interest how many observations do you have?