Robust outlier detection and estimation in response surface methodology

This thesis provides some extensions to the existing method of determining the optimization conditions in response surface design to cover situations with an unusual observations or outliers. It is shown how the presence of outliers have an unduly effect on the parameter estimation of response surface models and the optimum mean response. In real practice, the usual assumptions that the distribution of experimental data is approximately normal and constant variances are difficult to achieve. The classical outlier diagnostic methods may not be suitable to correctly diagnose the existence of outliers in a data set. To rectify this problem, two procedures of robust diagnostic methods are proposed. In response surface optimization methodology, the parameters of the model are usually estimated using the Ordinary Least Squares (OLS) technique. Nevertheless, the classical OLS suffers a huge set back in the presence of outliers. In this situation, the optimum response estimator is not reliable. As an alternative, we propose using a robust MM-estimator to estimate the parameters of the RSM and subsequently the optimum mean response is determined. The results of the study reveal that our proposed method outperforms some of the existing methods. This thesis also addresses the problems in the optimization of multiresponses,each of which depends upon a set of factors. The desirability function approach is commonly used in industry to tackle multiple response optimization problems. The shortcoming of this approach is that the variability in each predicted response is ignored. An augmented approach to the desirability function (AADF) is put forward to rectify this problem and to improve the practicality of the optimal solutions. Furthermore, the AADF can reduce the variation of predicted responses, as well as it is resistant to outliers. In robust design studies, the usual assumptions of experimental data are approximately normal and there is no major contamination due to outliers in the data. In real practice, these two assumptions are difficult to meet. Hence we proposed Two-Stage Robust MM (TSR-MM based) method where it can remedy both problem of heteroscedasticity and outliers at the same time. In order to make significant improvements in robust design studies, robust location (median) and robust scales estimates (Median Absolute Deviation (MAD) and Interquartile Range (IQR)) of the response variables are employed for dual response surface optimization. To get more efficient results, we proposed to adopt the robust MM estimator and the TSR-MM based method based on robust location and robust scales estimates when the problem of heteroscedastic errors comes together with outliers. The results of the study indicate that the robust location and scales estimates provide a significant reduction in the bias and variance of the estimated mean response.

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