Nonlinear Profile Monitoring Using Spline Functions
In this study, two new integrated control charts, named <inline-formula><math display="inline"><semantics><msup><mi>T</mi><mn>2</mn></msup></semantics></math></inline-formula>-MAE chart and MS-MAE chart, are introduced...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/9/1588 |
| _version_ | 1797553680160915456 |
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| author | Hua Xin Wan-Ju Hsieh Yuhlong Lio Tzong-Ru Tsai |
| author_facet | Hua Xin Wan-Ju Hsieh Yuhlong Lio Tzong-Ru Tsai |
| author_sort | Hua Xin |
| collection | DOAJ |
| description | In this study, two new integrated control charts, named <inline-formula><math display="inline"><semantics><msup><mi>T</mi><mn>2</mn></msup></semantics></math></inline-formula>-MAE chart and MS-MAE chart, are introduced for monitoring the quality of a process when the mathematical form of nonlinear profile model for quality measure is complicated and unable to be specified. The <inline-formula><math display="inline"><semantics><msup><mi>T</mi><mn>2</mn></msup></semantics></math></inline-formula>-MAE chart is composed of two memoryless-type control charts and the MS-MAE chart is composed of one memory-type and one memoryless-type control charts. The normality assumption of error terms in the nonlinear profile model for both proposed control charts are extended to a generalized model. An intensive simulation study is conducted to evaluate the performance of the <inline-formula><math display="inline"><semantics><msup><mi>T</mi><mn>2</mn></msup></semantics></math></inline-formula>-MAE and MS-MAE charts. Simulation results show that the MS-MAE chart outperforms the <inline-formula><math display="inline"><semantics><msup><mi>T</mi><mn>2</mn></msup></semantics></math></inline-formula>-MAE chart with less false alarms during the Phase I monitoring. Moreover, the MS-MAE chart is sensitive to different shifts on the model parameters and profile shape during the Phase II monitoring. An example about the vertical density profile is used for illustration. |
| first_indexed | 2024-03-10T16:20:01Z |
| format | Article |
| id | doaj.art-db1d8d597704429bbe807492cccf1491 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T16:20:01Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-db1d8d597704429bbe807492cccf14912023-11-20T13:47:28ZengMDPI AGMathematics2227-73902020-09-0189158810.3390/math8091588Nonlinear Profile Monitoring Using Spline FunctionsHua Xin0Wan-Ju Hsieh1Yuhlong Lio2Tzong-Ru Tsai3School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, ChinaDepartment of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, TaiwanDepartment of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USADepartment of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, TaiwanIn this study, two new integrated control charts, named <inline-formula><math display="inline"><semantics><msup><mi>T</mi><mn>2</mn></msup></semantics></math></inline-formula>-MAE chart and MS-MAE chart, are introduced for monitoring the quality of a process when the mathematical form of nonlinear profile model for quality measure is complicated and unable to be specified. The <inline-formula><math display="inline"><semantics><msup><mi>T</mi><mn>2</mn></msup></semantics></math></inline-formula>-MAE chart is composed of two memoryless-type control charts and the MS-MAE chart is composed of one memory-type and one memoryless-type control charts. The normality assumption of error terms in the nonlinear profile model for both proposed control charts are extended to a generalized model. An intensive simulation study is conducted to evaluate the performance of the <inline-formula><math display="inline"><semantics><msup><mi>T</mi><mn>2</mn></msup></semantics></math></inline-formula>-MAE and MS-MAE charts. Simulation results show that the MS-MAE chart outperforms the <inline-formula><math display="inline"><semantics><msup><mi>T</mi><mn>2</mn></msup></semantics></math></inline-formula>-MAE chart with less false alarms during the Phase I monitoring. Moreover, the MS-MAE chart is sensitive to different shifts on the model parameters and profile shape during the Phase II monitoring. An example about the vertical density profile is used for illustration.https://www.mdpi.com/2227-7390/8/9/1588cubic B-spline approximationHotelling <i>T</i><sup>2</sup> chartmaximum likelihood estimatemultivariate exponentially weighted moving averagestatistical process control |
| spellingShingle | Hua Xin Wan-Ju Hsieh Yuhlong Lio Tzong-Ru Tsai Nonlinear Profile Monitoring Using Spline Functions Mathematics cubic B-spline approximation Hotelling <i>T</i><sup>2</sup> chart maximum likelihood estimate multivariate exponentially weighted moving average statistical process control |
| title | Nonlinear Profile Monitoring Using Spline Functions |
| title_full | Nonlinear Profile Monitoring Using Spline Functions |
| title_fullStr | Nonlinear Profile Monitoring Using Spline Functions |
| title_full_unstemmed | Nonlinear Profile Monitoring Using Spline Functions |
| title_short | Nonlinear Profile Monitoring Using Spline Functions |
| title_sort | nonlinear profile monitoring using spline functions |
| topic | cubic B-spline approximation Hotelling <i>T</i><sup>2</sup> chart maximum likelihood estimate multivariate exponentially weighted moving average statistical process control |
| url | https://www.mdpi.com/2227-7390/8/9/1588 |
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