On the inadequacy of the customary orthogonal arrays in quality control and general scientific experimentation, and the need of probing designs of higher revealing power ∗
This paper breaks new ground concerning the general problem of factorial experimentation, namely, the identification and estimation of nonnegligible factorial effects (with minimal number of runs), without making the usual unrealistic and artificial assumptions concerning the negligibility of higher order interactions. (In other words, we consider the general factor screening problem when interactions may be present.) Through an example, it is shown that the customary orthogonal arrays fall short of the need. New principles for sieving the set of factorial effects to determine the large ones, are introduced. The concept of ‘revealing power’of designs, i.e. of their ability to help identify nonnegligible parameters is developed, and the usefulness in this direction of balanced arrays of full strength is studied.