Abstract
Abstract: Multivariate control charts are essential tools in multivariate statistical process control (MSPC). “Shewhart-type” charts are control charts using rational subgroupings which are effective in the detection of large shifts. Recently, the one-class classification problem has attracted a lot of interest. Three methods are typically used to solve this type of classification problem. These methods include the k−center method, the nearest neighbor method, one-class support vector machine (OCSVM), and the support vector data description (SVDD). In industrial applications, like statistical process control (SPC), practitioners successfully used SVDD to detect anomalies or outliers in the process. In this paper, we reformulate the standard support vector data description and derive a least squares version of the method. This least-squares support vector data description (LS-SVDD) is used to design a control chart for monitoring the mean vector of processes. We compare the performance of the LS-SVDD chart with the SVDD and T2 chart using out-of-control Average Run Length (ARL) as the performance metric. The experimental results indicate that the proposed control chart has very good performance.
Highlights
Due to recent advances in computing and availability of big data, the area of Statistical Process Monitoring (SPM) and Statistical Process Control (SPC) is facing a lot of challenges in dealing with these large data sets
The LS-support vector data description (SVDD) will ease the design of control charts using support vector methods and opens the doors to more advanced improvement of control charts using support vector methods. We propose another approach to solve the dual problem of the least-squares support vector data description (LS-SVDD) without using quadratic programming solvers as suggested by Guo et al (2017)
The Hotelling T2 chart is a parametric control chart that is optimum for multivariate normal data whereas the LS-SVDD and SVDD are both nonparametric methods that can be used for any distribution
Summary
Due to recent advances in computing and availability of big data, the area of Statistical Process Monitoring (SPM) and Statistical Process Control (SPC) is facing a lot of challenges in dealing with these large data sets. Because of the use of quadratic programming in solving LS-SVDD by Guo et al (2017), their proposal has the same computational cost as SVDD (Tax & Duin, 1999) and does not achieve the main goals of least squares support vector methods. Note that all existing control charts based on support vector methods solve long and computationally hard quadratic programming problems. The proposed control chart is the first support vector control chart which doesn’t use a computationally expensive quadratic programming solver Instead, it uses a closed form solution and simplifies the computational burden. To derive least squares version of the support vector data description, we reformulate the SVDD described in (2.1) by using a quadratic error function and equality constraints. The section will propose a new way to get to the same solution of Guo et al (2017), without using a quadratic programming solver
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
