Obtaining sequences of lower cost factorial experiments 2k-p applying mathematical programming methods

Abstract

Continuous improvement is part of management programs, such as Total Quality and Six Sigma. Statistical techniques have a central role in projects for improvement, particularly in Design of Experiments (DOE). DOE is a methodology that specifies the sequence of experiments to be performed, allowing a set of variables to con- trol one or more variables of response. From these experiments, it is possible to develop a mathematical model that allows inferring the result from a combination of variables. Each sequence can be evaluated according to some measure of costs, such as the number of changes of variables in the transition between two experiments, or maximum counting time. Since the complete enumeration of all possible sequences with 16 or more experi- ments demands considerable computational effort, we suggest the application of mathematical programming approaches to provide a sequence with minimal number of changes of variables. The problem was modeled as a modified traveling salesman problem, and implemented in GAMS/CPLEX modeling language. The method was applied to a case and MDV and MCT results were calculated and compared to the randomized sequences of the experiments and default order. The sequence obtained by the method reduced experimentation time by 43%, however the proposal sequence was less robust to effects of trends than the randomized sequence. Keywords: Continuous Improvement, DOE, Design of Experiments