Design Of The Improved EWMA Schemes For Monitoring The Ratio Of Two Normal Random Variables

Product quality has become one of the important factors when consumers choose products or service.Improving product quality is the key for enterprises to improve their competitiveness and succeed.Statistical Process Control(SPC),as an effective tool for quality management,can analyze and evaluate the production process,timely identify and eliminate the abnormal situation in the process,and improve the product percent of pass.As one of the important tools of SPC,control chart is often used to monitor and analyze the quality characteristics of products in the process,improve the product quality and ultimately cut back production costs for enterprises.In recent years,the research on the control chart for monitoring the ratio of two normal variables(RZ)is one of the important directions of SPC,which plays a significant part in the actual production process.In production scenarios,when the product specification is related to the relative ratio of two components in a mixture,or when the ratio represents the quality characteristics of the product,or the difference between a product’s quality measurement before and after an operation(such as a chemical reaction),the control chart for monitoring the RZ can be applied to ensure the stability of the process and make the product quality meet the production expectations.The traditional Shewhart chart is weak in monitoring the small or moderate shifts in the process,while the Exponentially Weighted Moving Average(EWMA)chart can improve the performance of the Shewhart chart by making full use of the previous samples’ information.To further improve the sensitivity of traditional RZ chart to small or moderate process shifts,based on the traditional EWMA-RZ chart,this dissertation puts forward several new EWMA schemes for monitoring the RZ.This dissertation proposes an Improved EWMA(IEWMA)control chart for monitoring the RZ.Monte-Carlo(MC)simulation is used to simulate the run length(RL)distribution of the proposed IEWMA-RZ control chart.Moreover,the IEWMA control chart parameters are optimized and the performance of the proposed IEWMA-RZ control chart is compared with that of the existing EWMARZ control chart.The simulation results show that the IEWMA-RZ control chart is perform better than the existing EWMA-RZ control chart in detecting process shifts,especially the small and moderate ones.The weight of "pumpkin seeds" and "flaxseeds" in food processing is monitored by an example of food processing plant,which further illustrates the superiority of the IEWMA control chart.Second,by weighting the smoothing coefficient of the EWMA-RZ control chart twice,this dissertation puts forward the Double EWMA(DEWMA)RZ control chart.Similarly,MC simulation is used to simulate the RL distribution of the DEWMA-RZ control chart.For different combinations of the chart parameters,this dissertation analyzes the performance of the DEWMA-RZ control chart in detail,and compares the performance of the proposed chart with the EWMA control chart.The simulation results show that the proposed DEWMA-RZ control chart is superior to the traditional EWMA-RZ control chart in small process shifts.The superiority of the proposed control chart is further illustrated by applying an example for a food processing plant.Third,the performance of the control chart can be improved by adopting Variable Sampling Interval(VSI)strategy in the actual production process,while the traditional RZ control chart usually adopts Fixed Sampling Intervals(FSI)strategy.Therefore,this dissertation further introduces the VSI strategy into the DEWMA-RZ control chart,and puts forward VSI-DEWMA-RZ control chart.Under different combinations of the chart parameters,the performances of VSI-DEWMA-RZ,VSI-EWMARZ and DEWMA-RZ control charts are analyzed and compared in this dissertation.The research results show that the VSI-DEWMA-RZ control chart is superior to DEWMA-RZ chart,and superior to the existing VSI-EWMA-RZ control chart for monitoring the small process shifts.The superiority of VSI-DEWMA-RZ control chart is further verified through the case of the food processing plant.Finally,based on the above study,by weighting the smoothing coefficient of the EWMA-RZ control chart triple and introducing VSI feature,this dissertation proposes the triple exponentially weighted moving average(Triple EWMA,TEWMA)RZ control chart and the VSI-TEWMA-RZ control chart,respectively.Similarly,MC simulation is used to simulate the RL distribution of the TEWMA-RZ and VSI-TEWMA-RZ control charts.Under different parameter combinations,the performance of the TEWMA-RZ and VSI-TEWMA-RZ control charts is analyzed in detail and compared with that of the EWMA-RZ control chart and related control charts.The results show that VSI-TEWMA-RZ performs better than TEWMA-RZ control chart.In addition,the VSI-TEWMARZ chart is more sensitive than the VSI-EWMA-RZ and VSI-DEWMA-RZ control charts in detecting the small shifts in a process.The performances of TEWMA-RZ and VSI-TEWMA-RZ control charts is further investigated by the example for food processing plants.