Stopping rules for sequences of factorial designs

When the sequential design of response surface and fractional factorial experiments was introduced in the 1950s, the question of deciding when to stop was raised but not answered. In this paper the decision is made using a Bayesian analysis, by obtaining the posterior distribution of the difference between the optimal response and the response from the predicted optimum. The experimentation is stopped, for example, when the mean of this posterior distribution falls below a specified value. The method works best if the variances of the prior distribution are not too low.