Second-order sub-array Cartesian product split-plot design
Colorado State University. Libraries
Fisher (1926) laid down the fundamental principles of design of experiments: factorization, replication, randomization, and local control of error. In industrial experiments, however, departure from these principles is commonplace. Many industrial experiments involve situations in which complete randomization may not be feasible because the factor level settings are impractical or inconvenient to change, the resources available to complete the experiment in homogenous settings are limited, or both. Restricted randomization due to factor levels that are impractical or inconvenient to change can lead to a split-plot experiment. Restricted randomization due to resource limitation can lead to blocking. Situations that require fitting a second-order model under those conditions lead to a second-order block split-plot experiment. Although response surface methodology has experienced a phenomenal growth since Box and Wilson (1951), the departure from standard methods to tackle second-order block split-plot design remains, for the most part, unexplored. Most graduate textbooks only provide a relatively basic treatise of the subject. Peer-reviewed literature is scarce, has a limited number of examples, and provides guidelines that often are too general. This deficit of information leaves practitioners ill prepared to face the roadblocks illuminated by Simpson, Kowalski, and Landman (2004). Practical strategies to help practitioners in dealing with the challenges presented by second-order block split-plot design are provided, including an end-to-end, innovative approach for the construction of a new form of effective and efficient response surface design referred to as second-order sub-array Cartesian product split-plot design. This new form of design is an alternative to ineffective split-plot designs that are currently in use by the manufacturing and quality control community. The design is economical, the prediction variance of the regression coefficients is low and stable, and the aliasing between the terms in the model and effects that are not in the model as well as the correlation between similar effects that are not in the model is low. Based on an assessment using well-accepted key design evaluation criterion, it is demonstrated that second-order sub-array Cartesian product split-plot designs perform as well or better than historical designs that have been considered standards up to this point.
Includes bibliographical references.
response surface methodology, split-plot design, restricted randomization, design of experiments