A Study On Distance Based Real-time Contrast Monitoring Methods

Quality is defined as characteristic to meet requirement.So monitoring the quality is to monitor characteristics.In the early ages,people usually paid attention to univariate characteristic,so the methods were called univariate monitoring.But people usually had various demand to a product,then more characteristics should be monitored.It is naturaly to apply univariate monitoring to all the characteristics,but it is not efficint and sometimes wrong.So all the characteristics should be monitored jointly.Traditional multivariate control charts were designed under normal assumption and performed well,but they would get bad performance when the data was nonnormal,then modern multivariate control charts based on machine learning performed better.Control charts for nonnormal data were usually designed for special data and would failed for other data.If we trate in control data and out of control data as two classes,one class classification turns monitoring porblem to classification problem when the two classes data are available.But out of control data was always not available in traditional monitoring process.Artificial contrast solved the porblem by generating data artificially,so it was affected by the artificial data.Real-time contrast avoid this affection by monitoring other statistics such as classification error rate instead of classifying and get better performance.We design control charts based on distance under the RTC framework and make contributions as follows:?1?Design control charts using LDA based distance and analyse the parameters.Linear discriminant anaysis is to find separating hyperplane to separate data points from different classes and get good performance under normal assumption.Trating the points separated in the same side eqully made the statistics based on classification less sensetive.Design LDA-D,LDA-D₀ and LDA-D₁ control charts based on the distance from data points to the LDA separating hyperplane under the RTC framework,and compare to LDA-a₀,LDA-p₀ and LDA-p₁ control charts based on classification probabilities.Then analyse the affection of parameters.?2?Design control charts using KLDA based distance.LDA performs bad when the data is not linear separable,then the nonlinear classifier performs better.Kernel trick is to map data from data space to feature space where the data points can be linear separable while the data is not linear separable in data space.Apply kernel trick to LDA will get KLDA.Design KLDA-D₀ and KLDA-D₁ control charts based on the distance from data points to the KLDA separating hyperplane and KLDA-a₀ control charts based on classification error rate under the RTC framework,and compare to SVDD control chart under nonnormal data.?3?Design control charts using KL divergence and weighted KL divergence.KL divergence measures the difference between two distributions in information theory and probability theory,it is also called KL distance.Design KLD control chart based on KL divergence under the RTC framework,and compare to SVDD control charts under nonnormal data.KL divergence trated data points equally and missed the information of time.To consider the effect of time,wighted KL divergence based on parameter ? was used here.Design WKLD control charts based on weighted KL divergence under the RTC framework,and compare to KLD control chart which is special case of WKLD control charts under nonnormal data.Choosing special value of ? would make WKLD control charts more efficient.