Online Monitoring Of Linear Profile Data Based On EWMA-CUSUM Control Chart

Statistical Process Control(SPC)is a quality management technique to ensure that products and services meet the specified requirements.It can provide quality technical guidance and help for "quality".The early theoretical research on SPC started from the monitoring of unary continuous point data.Now the theoretical research on SPC has been enriched from unary to multivariate and high-dimensional data flow,from continuous data to discrete data,from point data to line data and plane data,and its theoretical research results have been very rich.With the development of modern industrial technology,the production process of precision manufacturing becomes more and more complex.The problems related to product precise can not be fully represented or explained by the mean or variance(or distribution)of a certain index or several indicators,but need to use profile data to describe the process more finely and completely.The on-line monitoring method for complex data like profile has become an important content of SPC research.Exponentially weighted moving average(EWMA)control charts and cumulative sum(CUSUM)control charts are very popular online monitoring methods.However,the monitoring effect of EWMA control chart will be affected by parameters.Larger parameters are more effective for large shifts,and smaller parameters are more effective for small shifts.When the parameters designed by CUSUM control chart do not consider the actual shift size,the control chart will perform very badly.However,when monitoring linear profile data online,the size of shift that often occurs is unknown.In order to improve the monitoring effect of control charts,a new adaptive EWMA-CUSUM control chart and multivariate EWMA(MEWMA)control chart are proposed in this paper,and the smoothing parameter is defined as a function of monitoring time.The smoothing parameters of the control chart are not fixed in the whole monitoring process,but are determined by the observed values.At each moment in the whole monitoring process,a larger smoothing parameter can be selected by the defined function when the shift is large,and a small smoothing parameter can be selected when the shift is small.Therefore,when the model shifts,the control chart can quickly send out an alarm signal.Through statistical simulation and empirical analysis,it is verified that the proposed adaptive control chart with variable smoothing parameters can effectively monitor a series of process shifts.For simple linear profile data and profile data with multiple response variables,the proposed method is compared with several classical monitoring methods after100,000 statistical simulations.Adjust the average run lengths of all control charts to 200 when they are in control,and compare their average run lengths when they are out of control.For simple linear profile data,the simulation results show that the average running length of the adaptive EWMA-CUSUM control chart and the MEWMA control chart are smaller and the monitoring performances are better when the monitoring process is out of control.For the linear profile data of multiple response variables,the simulation results show that the average running length of the adaptive MEWMA control chart is smaller and the monitoring performance is better when the monitoring process is out of control.The cases of simple linear and multi-response variables are empirically analyzed by chemical industry gas sensor data and hydraulic press pressure data,respectively.The results show that adaptive EWMA-CUSUM control chart and MEWMA control chart can deliver out-ofcontrol alarms quickly.