Quantifying the maximum possible improvement in $$2^{k}$$ 2 k experiments

Abstract

Abstract This research formulates, and numerically quantifies the optimal response that can be discovered in a design space characterized by main effects, and two-way and three-way interactions. In an experimental design setup, this can be conceptualized as the response of the best treatment combination of a

$$2^k$$

2 k

full factorial design. Using Gaussian and Uniform priors for the strength of main effects and interaction effects, this study enables a practitioner to make estimates of the maximum possible improvement that is possible through design space exploration. For basic designs up to two factors, we construct the full distribution of the optimal treatment. Whereas, for values of

$$k\ge 3$$

k ≥ 3

, we analytically formulate two indicators of a greedy heuristic of the expected value of the optimal treatment. We present results for these formulations up to

$$k=7$$

k = 7

factors and validate these through simulations. Finally, we also present an illustrative case study of the power loss in disengaged wet clutches, which confirms our findings and serves as an implementation guide for practitioners.