Methods Research On Nonparametric Control Chart For Multivariate Processes

For most control charts,we often need to assume that the observed values of a process follow a specific probability distribution(e.g.,Normal distribution).Therefore,the techniques applied to them are parametric,and influenced by the distribution assumptions.However,the distribution pattern of data and the complex relationship between data are difficult to assume arbitrarily and thus lead to false warning for corresponding parametric techniques based control charts.Therefore,it is critical to develop nonparametric methods that do not make any specific assumptions about the distribution of processes.In the context of high–speed data collection,in order to solve the problem of simultaneous monitoring in high–dimensional and further improve the detection efficiency of control charts,this paper discussed the following three aspects of work based on the existing research results:(1)For multivariate processes with unknown distribution,this paper discusses the properties of rank method,and proposes a new multivariate rank–based nonparametric Exponenially Weighted Moving Average(EWMA)control chart.The proposed method is compared with a recently proposed multivariate data–depth based nonparametric control chart in a series of simulations.When the data are normally distributed and change point is 100,RMI of the proposed control chart is 0.04.And RMI of the multivariate data–depth based nonparametric control chart is 0.27.Then,when is 200,RMI of the proposed method and the multivariate data–depth based nonparametric control chart are 0.16 and 0.41,respectively.When is 300,RMI of the proposed control scheme and multivariate data–depth based nonparametric control chart are 0.24 and 0.31,respectively.For other types of distributions,the proposed control chart still has smaller RMI than multivariate data–depth based nonparametric control chart for a range of shifts.Comprehensive analysis shows that the proposed multivariate nonparametric EWMA control chart is effective in detecting the location parameter shifts for the multivariate process.Finally,on the one hand,the proposed multivariate nonparametric EWMA control chart is applied to the analysis of influenza data.The example shows that the proposed method can accurately detect the changes of influenza data.On the other hand,we applied the proposed multivariate rank–based nonparameters control chart with cautious parameter learning(MEWMA–CP)to monitor and analyze power data.The results show that the mean absolute percentage error decreases by 4.6% at each time point every day of the Radial Basis Function Neural Network(RBF–NN)based prediction model and the average absolute percentage error of the Least Square Support Vector Machine Regression(LS–SVMR)based prediction model is decreases by 7.5% at each time point every day with the MEWMA–CP control chart monitoring.(2)In the context of high–speed data collection,the data has the characteristics of high dimensions and the overall distribution form is poorly understood,so the typical assumptions required by the traditional control chart are unlikely to be satisfied by the current process.Due to the limited data collection and processing capacity of the system at the same time(e.g.,much less sensors and the ability to analyze high–dimensional data at each moment is limited),we need to detect the shift in a process timely.On the one hand,based on the proposed dynamic sensor distribution strategy,this paper discusses the rank–based nonparametric - local Cumulative Sum(CUSUM)monitoring strategies.Meanwhile,the optimal parameter settings of the monitoring strategies are discussed through a series of simulations.The simulation results show that the proposed control chart is effective for the shift of location parameters.The simulation results show that the nonparametric CUSUM control chart has a poor performance for detecting small shifts( ≤ 1).However,the detection efficiency for medium and large shifts is still better.In general,when dimension is small,the proposed nonparametric CUSUM control scheme has a good performance in detecting location parameter shifts.With the increase of dimension ,the detection efficiency of the proposed control chart for small shifts is decreased.Finally,the proposed control chart is applied to monitor and analyze the actual medical data.On the other hand,based on the existing studies,this paper further considers the autocorrelation of high–dimensional data streams.This paper converts the continuous data streams into binary sequences,and calculates the autocorrelation coefficients of binary sequences.Then,we deduce the monitoring statistics of nonparametric CUSUM control chart for simultaneous monitoring location parameters and scale parameters,which is based on the likelihood ratio test.Finally,the detection efficiency of the proposed method is compared with that of the existing methods by simulation.Finally,this paper compares the detection efficiency of the proposed control chart with that of the existing method by simulation when ∈ {0.25,0.5,0.75}.The simulation results show that when the correlation coefficient is small,the detection performance of our proposed control chart is relatively better for different change points.However,when becomes larger,the detection efficiency of the proposed control chart is reduced.(3)For simultaneous monitoring strategies with unknown distribution in multivariate processes,this paper proposes a Shewhart control chart that based on the existing Lepage statistics.The proposed Shewhart control chart can simultaneously monitor location parameters and scale parameters.This paper discusses the method of dimensionality reduction for multivariate data.Then,we transform multivariate data into one–dimensional data that can be ”sorted”.And the Shewhart control chart for simultaneous monitoring location parameters and scale parameters is obtained,which the Shewhart control chart is based on the Mood statistics and Wilcoxon statistics of nonparametric hypothesis testing.Meanwhile,this paper gives the limiting properties of Mood statistics and Wilcoxon statistics and discusses the ircorrelation between the Mood statistics and Wilcoxon statistics.In this paper,the detection efficiency of the proposed control chart is analyzed and compared with the recently existing methods by simulation.Finally,the proposed control chart is applied to the monitoring and analysis of two actual data.This paper analyzes the detection efficiency of our proposed control chart under the multivariate normal distribution,multivariate distribution,multivariate exponential distribution and multivariate gamma distribution.Meanwhile,we compare the detection efficiency of the proposed control chart with that of recent existing methods.The simulation results show that the detection performance of the proposed control chart scheme is better for simultaneous monitoring the location and scale parameters shifts in a certain range.Finally,the proposed control chart is applied to the monitoring and analysis two actual data.