Designing fractional factorial split-plot experiments using integer programming

Journal of Quality Technology

2023

The family of orthogonally minimally aliased response surface or OMARS designs comprises traditional response surface designs, such as central composite designs and Box-Behnken designs, as well as definitive screening designs. Key features of OMARS designs are the facts that they are orthogonal for the main effects and that the main effects are not at all aliased with any two-factor interaction effect or with any quadratic effect. In this article, we present a method to arrange the runs of an OMARS design in blocks of equal size, so that the main effects can be estimated independently from the blocks, and the interaction effects and the quadratic effects are confounded as little as possible with the blocks. We show that our new method for blocking OMARS designs offers much flexibility when it comes to choosing the number of runs, the number of blocks and the block sizes, and that it sometimes yields better blocking arrangements of definitive screening designs than the method of Jones and Nachtsheim (2016).

Section: Mixed Integer Linear Programming Approachmentioning

confidence: 99%

Blocking OMARS designs and definitive screening designs

Ares

Journal of Quality Technology

2023

“…Recently, integer programming techniques have been used on multiple occasions in the context of optimal design of experiments. Capehart et al (2011) uses integer programming to design regular fractional factorial split-plot experiments, while Sartono et al (2015b) use integer programming to block given regular and nonregular orthogonal designs. Capehart et al (2012) and Sartono et al (2015a) use integer programming to construct blocked fractional factorial split-plot designs and general orthogonal fractional factorial split-plot designs, respectively.…”

Section: Time Trends and Optimal Design Of Experimentsmentioning

confidence: 99%

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

Ares

Journal of Quality Technology

2019

When a multi-factor 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 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 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 programming 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.

Section: An Artificial Experiments Involving a Pure-level Oamentioning

confidence: 99%

Blocking Orthogonal Designs With Mixed Integer Linear Programming

Sartono¹,

Schoen²,

2014

Technometrics

We present a mixed integer linear programming approach to orthogonally block two-level, multi-level and mixed-level orthogonal designs. The approach involves an exact optimization technique which guarantees an optimal solution. It can be applied to many problems where combinatorial methods for blocking orthogonal designs cannot be used. By means of 54run and 64-run examples, we demonstrate that our approach outperforms two benchmark techniques in terms of the number of estimable two-factor interaction contrasts and in terms of the D-efficiency for models with main effects and some two-factor interaction contrasts. We demonstrate the generic nature of our approach by applying it to the most challenging instances in a catalog of all orthogonal designs of strength 3 with up to 81 runs as well as a small catalog of strength-4 designs. The approach can also be applied to strength-2 designs, but, for these cases, alternative methods described in the literature may perform equally well. Supplementary materials for this article are available online.