A Practical Solution to the Small Sample Size Bias and Uncertainty Problems of Model Selection Criteria in Two-Input Process Multiple Response Surface Methodology Datasets

Abstract

Multiple response surface methodology (MRSM) most often involves the analysis of small sample size datasets which have associated inherent statistical modeling problems. Firstly, classical model selection criteria in use are very inefficient with small sample size datasets. Secondly, classical model selection criteria have an acknowledged selection uncertainty problem. Finally, there is a credibility problem associated with modeling small sample sizes of the order of most MRSM datasets. This work focuses on determination of a solution to these identified problems. The small sample model selection uncertainty problem is analysed using sixteen model selection criteria and a typical two-input MRSM dataset. Selection of candidate models, for the responses in consideration, is done based on response surface conformity to expectation to deliberately avoid selection of models using the problematic classical model selection criteria. A set of permutations of combinations of response models with conforming response surfaces is determined. Each combination is optimised and results are obtained using overlaying of data matrices. The permutation of results is then averaged to obtain credible results. Thus, a transparent multiple model approach is used to obtain the solution which gives some credibility to the small sample size results of the typical MRSM dataset. The conclusion is that, for a two-input process MRSM problem, conformity of response surfaces can be effectively used to select candidate models and thus the use of the problematic model selection criteria is avoidable.