An integer linear programing approach to find trend-robust run orders of experimental designs

Abstract

When a multifactor experiment is carried out over a period of time, the responses may depend on a time trend. Unless the tests of the experiment are conducted in proper order, the time trend has a negative impact on the precision of the estimates of the main effects, the interaction effects, and the quadratic effects. A proper run order, called a trend-robust run order, minimizes the confounding between the effects’ contrast vectors and the time trend’s linear, quadratic, and cubic components. Finding a trend-robust run order is essentially a permutation problem. We develop a multistage approach based on integer programing to find a trend-robust run order for any given design. The multistage nature of our algorithm allows us to prioritize the trend robustness of the main-effect estimates. In the literature, most of the methods used are tailored to specific designs and are not applicable to an arbitrary design. Additionally, little attention has been paid to trend-robust run orders of response surface designs, such as central composite designs, Box–Behnken designs, and definitive screening designs. Our algorithm succeeds in identifying trend-robust run orders for arbitrary factorial designs and response surface designs with two up to six factors.