Number of cycles in evolutionary operation

Abstract

Evolutionary operation (EVOP) proposed by Box (1957) is a method for continuous monitoring and improvement of a full-scale manufacturing process with the objective of moving the operating conditions toward the better ones. EVOP consists of systematically making small changes in the levels of the two or three process variables under consideration. Data are collected on the response variable at each point of two level factorial design with the center point and a cycle is said to have been completed. The cycles are replicated sequentially until the decision is made on whether further cycle of experiments is needed to conclude the significance of any of main effects or interaction effects or the curvature. In this paper, an improved flow chart of EVOP is proposed and how to determine the number of cycles is studied based on the size of type II error. In order to reject the alternative hypothesis of interests with more confidence and conclude that we believe in the null hypothesis of no effects, we propose a counter measure p*-value corresponding to the p-value. The relationship of p*-value to the probability of type II error beta under the alternative hypothesis of interests is analogous to that of p-value to the probability of type I error alpha. Also the implementation of EVOP with a mixture experiment is discussed.