In this paper, we obtain balanced resolution V plans for 2m factorial experiments (4 ≤ m ≤ 8), which have an additional feature. Instead of assuming that the three factor and higher order effects are all zero, we assume that there is at most one nonnegligible effect among them; however, we do not know which particular effect is nonnegligible. The problem is to search which effect is non-negligible and to estimate it, along with estimating the main effects and two factor interactions etc., as in an ordinary resolution V design. For every value of N (the number of treatments) within a certain practical range, we present a design using which the search and estimation can be carried out. (Of course, as in all statistical problems, the probability of correct search will depend upon the size of “error” or “noise” present in the observations. However, the designs obtained are such that, at least in the noiseless case, this probability equals 1.) It is found that many of these designs are identical with optimal b...

Balanced 2m factorial designs of resolution v which allow search and estimation of one extra unknown effect, 4 ≤ m ≤ 8

A brief introduction to oprimal design theorv is given for those who are not familiar with the subject. A list of 312 selected articles on the theory of optimal design is provided. The bibliography should be sufficiently thorough to be of use to researchers in the field.

An Introduction to Design Optimality with an Overview of the Literature.

Balanced arrays of strength 4 and balanced fractional 3m factorial designs

Characteristic polynomials of the information matrices of balanced fractional 3m factorial designs of resolution v

Search designs for 2m factorials derived from balanced arrays of strength 2(l+1) and ad-optimal search designs

In this paper, we present a class of fractional factorial designs of the 27 series, which are of resolutionV. Such designs allow the estimation of the general mean, the main effects and the two factors interactions (29 parameters in all for the 27 factorial) assuming that the higher order effects are negligible. For every value ofN (the number of runs) such that 29≦N≦42, we give a resolutionV design that is optimal (with respect to the trace criterion) within the subclass of balanced designs. Also, for convenience of analysis, we present for each design, the covariance matrix of the estimates of the various parameters. As a by product, we establish many interesting combinatorial theorems concerning balanced arrays of strength four (which are generalizations of orthogonal arrays of strength four, and also of balanced incomplete block designs with block sizes not necessarily equal).

D. V. Chopra

Papers

Optimal balanced 27 fractional factorial designs of resolution V, 49 ≤ N ≤55