ENBIS-17 in Naples

9 – 14 September 2017; Naples (Italy) Abstract submission: 21 November 2016 – 10 May 2017

Classes of Second Order Split-Plot Designs

11 September 2017, 12:30 – 13:00

Abstract

Submitted by
Jens Bischoff
Authors
Luis A. Cortes (MITRE Corporation), James R. Simpson (JK Analytics)
Abstract
Fisher (1926) laid down the fundamental principles of experiment design: factorization, replication, randomization, and local control of error. In many industries however, departure from these principles is commonplace. Often in our experiments complete randomization is not feasible because the factor level settings are hard, impractical, or inconvenient to change or the resources available to execute under homogeneous conditions are limited. These restrictions in randomization lead to split-plot experiments. We are also often interested in fitting second-order models leading to second-order split-plot experiments. Although response surface methodology has grown tremendously since 1951, the lack of alternatives for second-order split-plots remains largely unexplored. The literature and textbooks offer limited examples and provide guidelines that often are too general. This deficit of information leaves practitioners ill prepared to face the many roadblocks associated with these types of designs.
This presentation provides practical strategies to help practitioners in dealing with second-order split-plot and by extension, split-split-plot experiments, including an innovative approach for the construction of a response surface design referred to as second-order sub-array Cartesian product split-plot design. This new type of design, which is an alternative to other classes of split-plot designs that are currently in use in defense and industrial applications, is economical, has a low prediction variance of the regression coefficients, and low aliasing between model terms. Based on an assessment using well accepted key design evaluation criterion, second-order sub-array Cartesian product split-plot designs perform as well as historical designs that have been considered standards up to this point.

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