Selection of nearly orthogonal blocks in ‘ad-hoc’ experimental designs

• Ad hoc experimental designs can be built by simultaneously optimizing two criteria
• Randomization of experiments does not correct a bad blocking
• Blocking a design must be taken into account with other criteria simultaneously
• With a genetic algorithm, the Pareto-optimal front to block a design is estimated

The problem of blocking experimental designs is addressed, for both factorial type designs and response surface designs (i.e. for discrete and continuous experimental domains).The focus is to arrange block as orthogonally as possible. To measure the uncorrelatedness between the block and the coefficient estimates, we use directly the corresponding covariance factors.Nevertheless, the blocking of the design may change the variance and covariance of estimates of the remaining coefficients. To take into account this effect, we add the D-criterion to the covariance factors when looking for a design.This defines a multicriteria problem that should be tackled as such because some of the case-studies show that a sequential approach (first to look for a D-optimal design and then block it) leads to designs which are not even D-optimal.With a genetic algorithm, the Pareto-optimal front of the competing criteria is estimated, with the aim of helping in the decision about the design to choose.