Study On Fuzzy Interval Mean Square Error Control Chart

Control chart plays an important role in economy,service industry,manufacturing industry and other fields.It can monitor whether the process parameters are deviated,so as to judge whether the production process is in control.The mean square error control chart has strong detection ability and high statistical performance,because the mean square error,as a comprehensive measure of mean deviation from target value and process variation,can monitor the deviation of process mean and standard deviation at the same time.As is known to all,the traditional control chart uses a single variable value for monitoring.With the advent of the era of big data,the types of data generation tend to be diversified,and more and more data are collected in the form of interval-valued.The usual practice is to build the control chart by averaging the single value data of the two endpoints of interval.Control charts designed in this way may lose some important information,or even cause misjudgment.Based on this,this paper studies the fuzzy interval mean square error control charts of interval-valued data,constructs control charts from ordinary interval-valued data and dependent interval-valued data respectively,and discusses the statistical performance of fuzzy interval mean square error control charts under two different interval-valued data.This paper first introduces the theoretical knowledge of fuzzy interval data,introduces the related research of fuzzy theory,then introduces the basic theory of control chart,gives the related principles of construction of control chart and the introduction of control chart evaluation index.Then the exponentially weighted moving average square error control chart is designed on the basis of the mean square error control chart.Secondly,for interval-valued,two fuzzy interval mean square error(FIMSE)control charts are designed to monitor the difference between the quality process mean and the target value,as well as the shifts between the process mean and variance,and Monte Carlo simulation method is used to calculate the average operating length(ARL)under different shifts values.The ARL of the new control chart is compared with the mean square error(MSE)control chart and the sample mean((?))control chart,and the proposed control chart is analyzed.From the results of simulation and empirical analysis,it is found that the statistical performance of FIMSE control chart is better than that of MSE control chart and (?) control chart.Finally,we consider combining the exponentially weighted moving average method with the fuzzy interval mean square error statistics,a weighted moving average fuzzy interval mean square error(EWMA FIMSE)control chart based on dependent interval-valued data is proposed.The EWMA FIMSE control chart was used to monitor the difference between the quality process mean value and the target value,as well as the shifts of the process mean and variance.Monte Carlo simulation method was used to calculate the average run length under different shifts values.Comparing the ARL of the new control chart with exponentially weighted moving average mean square error(EWMA MSE)control charts and exponentially weighted moving average mean(EWMA (?))control charts,then an empirical analysis is made on the proposed control chart.The results of simulation and empirical analysis show that the statistical performance of EWMA FIMSE control chart is superior to EWMA MSE control chart and EWMA (?) control chart.