Nonlinear Profile Monitoring Using Spline Functions

Hua Xin, Wan-Ju Hsieh, Yuhlong Lio and Tzong-Ru Tsai
Additional contact information
Hua Xin: School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, China
Wan-Ju Hsieh: Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan
Yuhlong Lio: Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA
Tzong-Ru Tsai: Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan

Mathematics, 2020, vol. 8, issue 9, 1-20

Abstract: In this study, two new integrated control charts, named T 2 -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 T 2 -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 T 2 -MAE and MS-MAE charts. Simulation results show that the MS-MAE chart outperforms the T 2 -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.

Keywords: cubic B-spline approximation; Hotelling T 2 chart; maximum likelihood estimate; multivariate exponentially weighted moving average; statistical process control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/9/1588/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/9/1588/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:9:p:1588-:d:413755

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().