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 surfa...

Full description

Saved in:

Bibliographic Details
Main Author:	Mustafa, Mohd Shafie
Format:	Thesis
Language:	English
Published:	2015
Subjects:	Outliers (Statistics) Robust statistics
Online Access:	http://psasir.upm.edu.my/id/eprint/58658/1/IPM%202015%207IR.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-upm-ir.58658
record_format	uketd_dc
spelling	my-upm-ir.586582018-01-26T04:18:38Z Robust outlier detection and estimation in response surface methodology 2015-10 Mustafa, Mohd Shafie 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. Outliers (Statistics) Robust statistics 2015-10 Thesis http://psasir.upm.edu.my/id/eprint/58658/ http://psasir.upm.edu.my/id/eprint/58658/1/IPM%202015%207IR.pdf application/pdf en public phd doctoral Universiti Putra Malaysia Outliers (Statistics) Robust statistics
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Outliers (Statistics) Robust statistics
spellingShingle	Outliers (Statistics) Robust statistics Mustafa, Mohd Shafie Robust outlier detection and estimation in response surface methodology
description	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.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Mustafa, Mohd Shafie
author_facet	Mustafa, Mohd Shafie
author_sort	Mustafa, Mohd Shafie
title	Robust outlier detection and estimation in response surface methodology
title_short	Robust outlier detection and estimation in response surface methodology
title_full	Robust outlier detection and estimation in response surface methodology
title_fullStr	Robust outlier detection and estimation in response surface methodology
title_full_unstemmed	Robust outlier detection and estimation in response surface methodology
title_sort	robust outlier detection and estimation in response surface methodology
granting_institution	Universiti Putra Malaysia
publishDate	2015
url	http://psasir.upm.edu.my/id/eprint/58658/1/IPM%202015%207IR.pdf
_version_	1747812221169172480

Robust outlier detection and estimation in response surface methodology

Similar Items