A Variation of the Standard Steepest Ascent Search Procedure for Response Surface Experiments

The results of this chapter lead to a modification of the standard stopping rule which breathes new life into the method of steepest ascent, but which is unfortunately not sufficient to effect a total resuscitation. As expected, there is no uniformly optimum stopping rule, nor even a uniformly best test statistic; both the optimum statistic and the optimum test level depend on the model parameters y1 and y2. One can, however, adopt a compromise rule which works reasonably well for all parameter combinations by testing at the 25% level with the statistic zn = 1/2(yn -yn-2). In many cases the loss incurred by the compromise rule is less than half that incurred by the existing rule; in the few cases where the compromise rule is less efficient, the difference in losses is small. Nevertheless, the compromise rule is nearly always inferior to the parameter-dependent optimum rule, and the optimum itself is not always desirable