The TSR-MM based on robust location and scales measures in dual response optimization in the presence of outliers and heteroscedastic errors
The dual response surface optimization approach is commonly used in an industrial process to simultaneously optimize the process sample mean and the process sample standard deviation functions.The short coming of this approach is that the sample mean and the sample variance are used to fit the p...
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| Format: | Article |
| Language: | English |
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Academy of Sciences Malaysia,Akademi Sains Malaysia
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/82609/1/The%20TSR-MM%20based%20on%20robust%20.pdf |
| _version_ | 1796981054767104000 |
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| author | Mustafa, Mohd Shafie Midi, Habshah |
| author_facet | Mustafa, Mohd Shafie Midi, Habshah |
| author_sort | Mustafa, Mohd Shafie |
| collection | UPM |
| description | The dual response surface optimization approach is commonly used in an industrial process to simultaneously optimize the process sample mean and the process sample standard deviation functions.The short coming of this approach is that the sample mean and the sample variance are used to fit the process mean and process variance functions based on the OLS method.However,these estimators are very sensitive to outliers or departures from the normality assumption.The OLS estimates do not give good results when both outliers and heteroscedastic errors exist concurrently. As a consequence,the optimum operating conditions may be located far from the true optimum values. 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.Two-stage robust estimator based on MM-estimator (TSR-MM based) based on robust location and robust scales estimates is proposed to simultaneously remedy the problem of heteroscedastic errors and outliers.The results of the study indicate that the TSR-MM based on robust location and scales estimates provide a significant reduction in the bias and variance of the estimated mean response. |
| first_indexed | 2024-03-06T10:32:07Z |
| format | Article |
| id | upm.eprints-82609 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T10:32:07Z |
| publishDate | 2019 |
| publisher | Academy of Sciences Malaysia,Akademi Sains Malaysia |
| record_format | dspace |
| spelling | upm.eprints-826092021-09-29T09:36:43Z http://psasir.upm.edu.my/id/eprint/82609/ The TSR-MM based on robust location and scales measures in dual response optimization in the presence of outliers and heteroscedastic errors Mustafa, Mohd Shafie Midi, Habshah The dual response surface optimization approach is commonly used in an industrial process to simultaneously optimize the process sample mean and the process sample standard deviation functions.The short coming of this approach is that the sample mean and the sample variance are used to fit the process mean and process variance functions based on the OLS method.However,these estimators are very sensitive to outliers or departures from the normality assumption.The OLS estimates do not give good results when both outliers and heteroscedastic errors exist concurrently. As a consequence,the optimum operating conditions may be located far from the true optimum values. 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.Two-stage robust estimator based on MM-estimator (TSR-MM based) based on robust location and robust scales estimates is proposed to simultaneously remedy the problem of heteroscedastic errors and outliers.The results of the study indicate that the TSR-MM based on robust location and scales estimates provide a significant reduction in the bias and variance of the estimated mean response. Academy of Sciences Malaysia,Akademi Sains Malaysia 2019 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/82609/1/The%20TSR-MM%20based%20on%20robust%20.pdf Mustafa, Mohd Shafie and Midi, Habshah (2019) The TSR-MM based on robust location and scales measures in dual response optimization in the presence of outliers and heteroscedastic errors. ASM Science Journal, 12 (spec. 1). pp. 310-319. ISSN 1823-6782 https://www.akademisains.gov.my/asmsj/article/the-tsr-mm-based-on-robust-location-and-scales-measures-in-dual-response-optimization-in-the-presence-of-outliers-and-heteroscedastic-errors/ |
| spellingShingle | Mustafa, Mohd Shafie Midi, Habshah The TSR-MM based on robust location and scales measures in dual response optimization in the presence of outliers and heteroscedastic errors |
| title | The TSR-MM based on robust location and scales measures in dual response optimization in the presence of outliers and heteroscedastic errors |
| title_full | The TSR-MM based on robust location and scales measures in dual response optimization in the presence of outliers and heteroscedastic errors |
| title_fullStr | The TSR-MM based on robust location and scales measures in dual response optimization in the presence of outliers and heteroscedastic errors |
| title_full_unstemmed | The TSR-MM based on robust location and scales measures in dual response optimization in the presence of outliers and heteroscedastic errors |
| title_short | The TSR-MM based on robust location and scales measures in dual response optimization in the presence of outliers and heteroscedastic errors |
| title_sort | tsr mm based on robust location and scales measures in dual response optimization in the presence of outliers and heteroscedastic errors |
| url | http://psasir.upm.edu.my/id/eprint/82609/1/The%20TSR-MM%20based%20on%20robust%20.pdf |
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