Monitoring Linear Profiles Using Support Vector Machine Algorithm

As an important implement in Quality Management, Statistical Process Control(SPC) monitors all phases in process using statistical techniques in order ensure andimprove the quality of products. The statistical technique here is any mathematicalstatistics algorithm which can be applied, mainly about the control charts theories.Both the univariate control charts and the multivariate control charts are based on thehypothesis that quality characteristics obey a monohydric or polyhydric randomlydistributed. However, the qualities of products (or process) can be better described bythe functions of quality characteristics and observed variables. The relationships arecalled profiles. Because the key quality characteristic is not the univariate or themultidimensional vector, control charts of the past are no longer suitable for theprocess of quality control. It is meaningful to study how to control the functions or theprofiles.With the rapid development of computer techniques, especially the MachineLearning (ML) algorithms, fresh nutrients are put into research of profile control. Thescope of application of control charts is enlarged by the advantage of ML that the MLalgorithms can’t be restricted by the distribution of original data. Among thealgorithms, Artificial neural network (ANN), Support Vector Machine (SVM) and theDecision Trees have been studied and applied in the field of profiles control. On thebasis of the SVM’s superiority when dealing with small high-dimensional samples,this paper proposes three new control methods combined the advantage of SupportVector Data Description (SVDD). These methods are used to monitor shifts in linearregression model’s coefficients and error variance in Phase II. Parameters ofrespective method are calculated by simulation, and the performance of the controlschemes are studied through numerical experiments. Compared with monitoringschemes based on ANN,T2control charts, EWMA/R control charts and EWMA-3control charts, the simulation results show that when detecting medium to large shiftsin model’s coefficients, control schemes based on SVM have obvious advantages.While monitoring error variance, control scheme based on SVDD is the best methodamong the control charts considered.