Augmented approach to desirability function based on MM estimator
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. It is now evident that the actual response may fall outside the acceptable region even th...
| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
AIP Publishing LLC
2012
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57452/1/Augmented%20approach%20to%20desirability%20function%20based%20on%20MM%20estimator.pdf |
| _version_ | 1825931615300222976 |
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| author | Midi, Habshah Mustafa, Mohd Shafie Fitrianto, Anwar |
| author_facet | Midi, Habshah Mustafa, Mohd Shafie Fitrianto, Anwar |
| author_sort | Midi, Habshah |
| collection | UPM |
| description | 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. It is now evident that the actual response may fall outside the acceptable region even though the predicted response at the optimal solution has a high overall desirability score. An augmented approach to the desirability function (AADF) is put forward to rectify this problem. Nevertheless the AADF is easily affected by outliers since the AADF is constructed based on the Ordinary Least Squares (OLS) estimate which is not resistant to outliers. As an alternative, we propose a robust MM-estimator to estimate the parameters of the Response Surface Model (RSM) and incorporated the estimated parameters in the augmented approach framework. A numerical example is presented to assess the performance of the AADF-MM based method. The numerical results signify that the AADF-MM based is more efficient than the AADF-OLS based method. |
| first_indexed | 2024-03-06T09:29:26Z |
| format | Conference or Workshop Item |
| id | upm.eprints-57452 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:29:26Z |
| publishDate | 2012 |
| publisher | AIP Publishing LLC |
| record_format | dspace |
| spelling | upm.eprints-574522017-09-27T10:46:55Z http://psasir.upm.edu.my/id/eprint/57452/ Augmented approach to desirability function based on MM estimator Midi, Habshah Mustafa, Mohd Shafie Fitrianto, Anwar 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. It is now evident that the actual response may fall outside the acceptable region even though the predicted response at the optimal solution has a high overall desirability score. An augmented approach to the desirability function (AADF) is put forward to rectify this problem. Nevertheless the AADF is easily affected by outliers since the AADF is constructed based on the Ordinary Least Squares (OLS) estimate which is not resistant to outliers. As an alternative, we propose a robust MM-estimator to estimate the parameters of the Response Surface Model (RSM) and incorporated the estimated parameters in the augmented approach framework. A numerical example is presented to assess the performance of the AADF-MM based method. The numerical results signify that the AADF-MM based is more efficient than the AADF-OLS based method. AIP Publishing LLC 2012 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57452/1/Augmented%20approach%20to%20desirability%20function%20based%20on%20MM%20estimator.pdf Midi, Habshah and Mustafa, Mohd Shafie and Fitrianto, Anwar (2012) Augmented approach to desirability function based on MM estimator. In: 20th National Symposium on Mathematical Sciences (SKSM20), 18-20 Dec. 2012, Palm Garden Hotel, Putrajaya, Malaysia. (pp. 1240-1247). 10.1063/1.4801272 |
| spellingShingle | Midi, Habshah Mustafa, Mohd Shafie Fitrianto, Anwar Augmented approach to desirability function based on MM estimator |
| title | Augmented approach to desirability function based on MM estimator |
| title_full | Augmented approach to desirability function based on MM estimator |
| title_fullStr | Augmented approach to desirability function based on MM estimator |
| title_full_unstemmed | Augmented approach to desirability function based on MM estimator |
| title_short | Augmented approach to desirability function based on MM estimator |
| title_sort | augmented approach to desirability function based on mm estimator |
| url | http://psasir.upm.edu.my/id/eprint/57452/1/Augmented%20approach%20to%20desirability%20function%20based%20on%20MM%20estimator.pdf |
| work_keys_str_mv | AT midihabshah augmentedapproachtodesirabilityfunctionbasedonmmestimator AT mustafamohdshafie augmentedapproachtodesirabilityfunctionbasedonmmestimator AT fitriantoanwar augmentedapproachtodesirabilityfunctionbasedonmmestimator |