Analysis of Response Surface Model Parameters with Bayesian Approach and Fuzzy Approach

Abstract

Response Surface Methodology (RSM) is a group of mathematical and statistical methods used for exploring the optimum operating conditions through statistical design of experiments. Obtaining the suitable analytical model between input variables and one or more responses is the main stage in RSM studies. When the response has replications, these replicated values may cause error. The proper modeling approach should be preferred according to the source of error, which is randomness or measurement error. In this study, Bayesian approach and fuzzy approach are used to estimate the model parameters in which the error becomes randomness and measurement error, respectively. The novelty of this study is analysis of response surface model parameters, which are obtained by using Bayesian approach and fuzzy approach, through interval analysis. The interpretation of model parameters and the comparison of modeling approaches are evaluated by interval arithmetic metrics. The suggested approaches are applied on replicated response measured two data sets and the results are discussed.