Detecting the process changes for multivariate nonlinear profile data

Jeh-Nan Pan, Chung-I Li, Meng Zhe Lu

Research output: Contribution to journalArticle

Abstract

In profile monitoring for a multivariate manufacturing process, the functional relationship of the multivariate profiles rarely occurs in linear form, and the real data usually do not follow a multivariate normal distribution. Thus, in this paper, the functional relationship of multivariate nonlinear profile data is described via a nonparametric regression model. We first fit the multivariate nonlinear profile data and obtain the reference profiles through support vector regression (SVR) model. The differences between the observed multivariate nonlinear profiles and the reference profiles are used to calculate the vector of metrics. Then, a nonparametric revised spatial rank exponential weighted moving average (RSREWMA) control chart is proposed in the phase II monitoring. Moreover, a simulation study is conducted to evaluate the detecting performance of our proposed nonparametric RSREWMA control chart under various process shifts using out-of-control average run length (ARL 1 ). The simulation results indicate that the SREWMA control chart coupled with the metric of mean absolute deviation (MAD) can be used to monitor the multivariate nonlinear profile data when a common fixed design (CFD) is not applicable in the phase II study. Finally, a realistic multivariate nonlinear profile example is used to demonstrate the usefulness of our proposed RSREWMA control chart and its monitoring schemes.

Original languageEnglish
JournalQuality and Reliability Engineering International
DOIs
Publication statusPublished - 2019 Jan 1

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Monitoring
Normal distribution
Control charts
Process change
Moving average
Regression model

All Science Journal Classification (ASJC) codes

  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research

Cite this

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title = "Detecting the process changes for multivariate nonlinear profile data",
abstract = "In profile monitoring for a multivariate manufacturing process, the functional relationship of the multivariate profiles rarely occurs in linear form, and the real data usually do not follow a multivariate normal distribution. Thus, in this paper, the functional relationship of multivariate nonlinear profile data is described via a nonparametric regression model. We first fit the multivariate nonlinear profile data and obtain the reference profiles through support vector regression (SVR) model. The differences between the observed multivariate nonlinear profiles and the reference profiles are used to calculate the vector of metrics. Then, a nonparametric revised spatial rank exponential weighted moving average (RSREWMA) control chart is proposed in the phase II monitoring. Moreover, a simulation study is conducted to evaluate the detecting performance of our proposed nonparametric RSREWMA control chart under various process shifts using out-of-control average run length (ARL 1 ). The simulation results indicate that the SREWMA control chart coupled with the metric of mean absolute deviation (MAD) can be used to monitor the multivariate nonlinear profile data when a common fixed design (CFD) is not applicable in the phase II study. Finally, a realistic multivariate nonlinear profile example is used to demonstrate the usefulness of our proposed RSREWMA control chart and its monitoring schemes.",
author = "Jeh-Nan Pan and Chung-I Li and Lu, {Meng Zhe}",
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AU - Li, Chung-I

AU - Lu, Meng Zhe

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N2 - In profile monitoring for a multivariate manufacturing process, the functional relationship of the multivariate profiles rarely occurs in linear form, and the real data usually do not follow a multivariate normal distribution. Thus, in this paper, the functional relationship of multivariate nonlinear profile data is described via a nonparametric regression model. We first fit the multivariate nonlinear profile data and obtain the reference profiles through support vector regression (SVR) model. The differences between the observed multivariate nonlinear profiles and the reference profiles are used to calculate the vector of metrics. Then, a nonparametric revised spatial rank exponential weighted moving average (RSREWMA) control chart is proposed in the phase II monitoring. Moreover, a simulation study is conducted to evaluate the detecting performance of our proposed nonparametric RSREWMA control chart under various process shifts using out-of-control average run length (ARL 1 ). The simulation results indicate that the SREWMA control chart coupled with the metric of mean absolute deviation (MAD) can be used to monitor the multivariate nonlinear profile data when a common fixed design (CFD) is not applicable in the phase II study. Finally, a realistic multivariate nonlinear profile example is used to demonstrate the usefulness of our proposed RSREWMA control chart and its monitoring schemes.

AB - In profile monitoring for a multivariate manufacturing process, the functional relationship of the multivariate profiles rarely occurs in linear form, and the real data usually do not follow a multivariate normal distribution. Thus, in this paper, the functional relationship of multivariate nonlinear profile data is described via a nonparametric regression model. We first fit the multivariate nonlinear profile data and obtain the reference profiles through support vector regression (SVR) model. The differences between the observed multivariate nonlinear profiles and the reference profiles are used to calculate the vector of metrics. Then, a nonparametric revised spatial rank exponential weighted moving average (RSREWMA) control chart is proposed in the phase II monitoring. Moreover, a simulation study is conducted to evaluate the detecting performance of our proposed nonparametric RSREWMA control chart under various process shifts using out-of-control average run length (ARL 1 ). The simulation results indicate that the SREWMA control chart coupled with the metric of mean absolute deviation (MAD) can be used to monitor the multivariate nonlinear profile data when a common fixed design (CFD) is not applicable in the phase II study. Finally, a realistic multivariate nonlinear profile example is used to demonstrate the usefulness of our proposed RSREWMA control chart and its monitoring schemes.

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