An adaptive sequential stopping rule for steepest ascent searches based on the Wiener process

Abstract

Designed experimentation has been taken as one of the first stages for process improvement. Under this exploration, it is possible to reach a scenario where optimization is feasible all along an ascent trajectory of improvement. The proper moment to stop individual experimentation in the steepest path is critical in terms of efficiency and productivity. Different strategies have been applied for this purpose. For example, the Myers and Khuri Stopping Rule, the Recursive Parabolic Stopping Rule and the Enhanced Recursive Parabolic Stopping Rule. These stopping procedures assume a certain parametric behavior when applied. The purpose of this paper is to present a new stopping rule that adapts to the behavior of the observed response without the need to make parametric assumptions to reach the best possible response. This new Adaptive Sequential Stopping Rule is based on a non-monotone stochastic process with a drift based on the Hjorth´s rate. All these stopping rules, including the new one, were applied in a simulated process and a case study to verify and compare their performances. The results were conclusive, the new Adaptive Sequential Stopping Rule adapted successfully to the behavior of the observed response showing a better performance than the currently used procedures.