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

When a multi-factor experiment is carried out over a period of time, the responses may suffer from a time trend. Unless the tests of the experiment are conducted in a 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 e ects. A proper run order, called a trend-robust run order, minimizes the correlation between the effects estimates and the time trend s linear, quadratic and cubic components. Finding a trend-robust run order is essentially a permutation problem. We develop a sequential approach based on integer programming to find a trend-robust run order for any given design. The sequential 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 sequential algorithm succeeds in identifying trend-robust run orders for arbitrary factorial designs and response surface designs with two up to six factors.