Multivariate Process Monitoring Schemes For Mixed-type Data

Statistical process control is one of the most important parts of quality management in the manufacturing or service industries.As an important tool in statistical process control,the control chart can comprehensively monitor the product manufacturing process and send abnormal in time.With the improvement of R&D technology and manufacturing process,higher requirements are put forward for the applicability and accuracy of the control chart.The dimension of monitoring data extends from one dimension to multi-dimensional,and the data types are also extended from numerical to mixed-type.Mixed-type data includes numerical and categorical variables.Categorical variables can be divided into ordinal and nominal types.Ordinal variables have only a certain level of characteristics,while nominal variables almost have no numerical attributes.The traditional multi-dimensional control chart schemes often do not consider categorical variables when dealing with mixed-type data,or directly convert categorical variables into numerical values,and then monitor them by numerical control charts.These methods are only applicable to scenes with small amount of categorical variables or unimportant categorical variables.In most cases,their monitoring effects are not satisfactory.For the current situation of mixed-type data control chart with large quantization difficulty and poor monitoring accuracy,this paper uses the rank correlation between ordinal variables and the attribute values' inhomogeneity of nominal variables and designs two corresponding mixedtype data control charts respectively,named RVC(R-Vine Copula,RVC)control chart and MLOF(Mixed-type data Local Outlier Factor,MLOF)control chart.The advantages of the new control charts over the existing control charts are proved by numerical simulations and real data cases.First of all,we introduce the background and significance of this study,then summarize the domestic and foreign literatures on multi-dimensional numerical data and mixed-type data control charts.The introductions of numerical data control charts are divided into normal continuous data,the non-normal continuous data and the count data.What's more,the control charts of mixed-type data with ordinal and nominal variables are shown in detail.At the same time,the paper analyzes the existing problems in mixedtype data monitoring and explains the main research contents and the framework of the full text.Secondly,this paper proposes an RVC control chart based on Copula model for mixed-type data monitoring problems with ordinal variables.There exists certain rank correlation between sequential variables and other variables,while Copula model can effectively describe the correlation between variables.According the study of the Copula model and its application in multi-dimensional data modeling,this paper selects the RVine Copula structure to model the mixed-type data.The kernel density estimation method is used to determine the marginal probability distribution function of each variable.Then the mixed-type data joint probability density function is obtained.The design of the control chart is finally completed.The better monitoring performance of proposed control chart than existing control charts is validated according to a real data case.Third,the existing mixed-type data distance measurement schemes are mostly applied to cluster analysis.There are many restrictions and huge computational burden when applied to the multi-dimensional data monitoring process.This paper designs a new mixed-type data distance measurement scheme.This scheme fully considers the rank of ordinal variables and the attribute values' inhomogeneity of of nominal variables.The distance between different types of variables are normalized reasonably.It provides a similarity measure basis for the design of MLOF control chart in the next text.Fourth,this paper combines the new mixed-type data distance measurement scheme with a data mining algorithm.It chooses the LOF algorithm to measure the degree of data anomaly.The application of the traditional LOF algorithm is expanded from numerical data to mixed-type data.A density-based MLOF mixed-type data control chart is designed.This control chart can effectively deal with the mixed-type data monitoring problem containing nominal variables.It can judge whether the observed data is in a controlled state by comparing the observed data statistics with the value of control limit.The simulation and real data case verify that the MLOF control chart is more suitable for the mixed-type data monitoring process with more nominal variables and obvious data clustering features.