Generalized maximum entropy approach to unreplicated factorial experiments

In the initial stage of developing an industrial process, experimental studies based on factorial designs are often used to determine which factors among a number of factors have an effect on the response variable. A large number of factors somehow may arise and a number of runs that grows exponentially with the number of factors to be analyzed. Therefore, researchers often design unreplicated factorial experiments. Furthermore, considering the cost of experimentation, time, effort, and/or limitation of data resources, unreplicated factorial designs can be adopted to reduce the number of runs. But, using ordinary least squares method to analyze unreplicated experimental data results in zero degrees of freedom for error term in regression analysis. Generalized maximum entropy approach which is a method of selecting among probability distributions to choose the distribution that maximizes uncertainty or uniformity remaining in the distribution, subject to information already known about the distribution, is an alternative way of analyzing the unreplicated experiments. In this paper, generalized maximum entropy approach is applied to an illustrative data set and a real-world example and results are compared to the alternatives with respect to their abilities to find active effects.

Keywords

design of experiments, generalized maximum entropy approach, ordinary least squares, unreplicated factorial designs

2010 Mathematics Subject Classification

Primary 62K15. Secondary 62J10.

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Published 27 January 2016