Variable Dimension Control Charts For Monitoring Process Mean Vector And Covariance Matrix

Control charts play an important role in the economy,service industry,manufacturing and other fields.It can monitor whether process parameters shifts and determine whether the production process is in-control.The multivariate control charts are widely used to detect assignable causes of processes with multiple quality characteristics.Among the multiple variables being monitored,there are often some variables that are easy to measure and/or inexpensive to measure,while remaining variables are difficult to measure and/or costly to measure.Moreover,the scheme of jointly monitoring the mean vector and covariance matrix is gaining more and more attention.Based on this,this paper investigates the statistical performance of two variable dimension control charts that jointly monitor process mean vectors and covariance matrices.This paper firstly introduces a variable dimension(denoted as VD)T ~2 control chart for monitoring the process mean.Sampling cost,and improve statistical performance,a new variable-dimension multivariate control chart is proposed,denoted as VD Max-type control chart,and the Markov chain model is used to calculate the average running length under different offset values(denoted as ARL),and then use genetic algorithm to optimize the parameters of VD Max-type control chart.On this basis,in order to reduce the sampling cost of multivariate control charts in detecting mean vector and covariance matrix shifts in the process of multivariate normal distribution,and improve statistical performance,a new variable dimension multivariate control chart is proposed,denoted as the VD Max-type control chart.This paper uses the Markov chain model to calculate the Average Run Length(ARL)and compares the performance of the VD Max-type control chart with the standard Max-type control chart with all variables measured.Numerical results show that the VD Max-type control chart outperforms the standard Max-type control chart while reducing the sampling cost.Secondly,an Exponentially Weighted Moving Average(EWMA)VD T ~2 control chart for monitoring the process mean is introduced.On the basis of VD Max-type control chart,combined with EWMA method,we propose a variable dimension Max-EWMA control chart for joint monitoring of mean vector and covariance matrix,denoted as VD Max-EWMA control chart.This paper uses the Markov chain model to calculate ARL and compares the performance of VD Max-EWMA control chart with VD Max-type control chart.Numerical results show that the VD Max-EWMA control chart performs better than the VD Max-type control chart,especially in detecting small and medium shifts,ARL improves significantly.Thirdly,the performance of the jointly monitored Max-type control chart under the seven schemes,variable sample size(VSS),variable sampling interval(VSI),variable sample size and sampling interval(VSSI),variable parameter(VP),EWMA,VD and VD Max-EWMA,is compared.Finally,the construction and realization process of the VD Max-EWMA control chart are explained by an example.