Research On Online Monitoring The Coefficient Of Variation

Control charting techniques are crucial process monitoring tools and have been widely used in practice.When we consider variable data,most control charts are used to monitor the process mean or standard deviation.However,not all process means or standard deviations are constant even though the process may be smoothly working within an acceptable range of dispersion.In this situation,we usually consider the coefficient of variation（CV）,which is defined as the ratioγof the standard deviationσto the meanμ.The CV is a dimensionless measure of the dispersion that is widely applied to measure the relative variation of a variable.When comparing the variations of several variables,the standard deviation is not a suitable measure of the variation unless the variables are all expressed in identical units of measurement and have the same mean.When the above requirements do not hold,the CV is more meaningful than the standard deviation for comparing the variability among several groups of observations.This paper systematically and comprehensively review the work of the control chart for monitoring the CV.It is shown that the proportion of the memory-type CV control charts is 37%of the total.Therefore,the memory-type control chart for the detection of the process shifts of the CV is an important subject for further research.In particular,the memory-type multivariable control charts for monitoring the CV only account for 1.3%of the total,and there are still some gaps,which is a potential field to be studied.Based on six models,nine new memory-type control charts are designed for monitoring the process shifts of the CV of the univariate and multivariable in Phase II.They are the OSRG control chart based on the generally weighted moving average（GWMA）model,the PCV chart and PRCV chart based on the progressive average（PA）model,based on the homogeneously weighted moving average（HWMA）model,the HS and HSI chart,the HCVT chart and the VSSI HCVT chart with variable sample size and sampling interval（VSSI）.For multivariable coefficient of variation（MCV）,the HWMA-MCV control chart and the VSI HWMA-MCV control chart with variable sampling interval（VSI）,are proposed respectively.When the processes are in control and out of control,the performances of the new control charts are analysed and compared with the existing control charts for the detection of the CV.The results show that the newly designed control charts are obviously better than other competitive charts,especially for the small and medium-sized shifts.Additionally,the application examples are given to further demonstrate the effectiveness and advantages of the proposed control charts.The full paper is divided into eight parts.The first chapter is the introduction,which mainly introduces the research background and significance,literature review,research content and methods,and innovation of this thesis.In Chapter 2,two one-sided GWMA control charts with adjusted time-varying control limits for monitoring the CV of a normally distributed process variable are proposed.The two control charts are constructed by combining the generally weight-ed moving average procedure with a resetting model.The implementations of the proposed charts are presented.Some numerical comparisons of the proposed charts with several relevant competing control charts are performed.In general,as demon-strated by extensive simulation results,our charts are clearly more sensitive than other competing procedures for each combination of the in-control target value of the CV,the sample size and the shift size.Detection examples are given for two industri-al manufacturing processes to introduce the proposed control charts.The proposed OSRG charts with fast initial response is an advantage.In Chapter 3,two progressive average control procedures are proposed for moni-toring the CV of a normally distributed process variable,namely the PCV and PRCV control charts,respectively.The implementations of the proposed charts are present-ed,and the necessary design parameters are provided.The effect on the performances of the PCV and PRCV control charts when the actual value of the CV varies within-5%～+5%of the given nominal value,and the effect of parameter estimation,are analysed.Through extensive numerical simulations,it is shown that the proposed PCV and PRCV charts outperform several existing control charts to detect the ini-tial out-of-control signals,especially for the small and moderate shifts,under each combination of the shift size,the sample size,and the in-control parameter value.Ad-ditionally,the application of the proposed control charts is illustrated by a detection example for a spinning process.The good features of the proposed PCV and PRCV charts are with fast initial response,and no additional parameters are required,so they are simple and handy.In Chapter 4,the HS and HSI control charts are proposed based on homoge-neously weighted moving average model.The HS and HSI control charts integrate the resetting program into the charts to improve the detection ability.The perfor-mance of the proposed control charts are analyzed in detail,and compared with the existing memory-type charts for monitoring the CV.It is shown that the HS chart is the most effective for detecting the downward shifts,and the HSI chart is superior to monitor the upward shifts.The HSI control chart adopt the normal inverse trans-formation technology,so that the statistics of the control chart can be transformed from the original biased distribution to the symmetrical standard normal distribu-tion.One of the biggest advantages of the HSI control chart is that the control limit is independent of the initial value of the parameterγ₀and sample size n.This brings great convenience to the use and for further development of the control chart.This characteristic has been a research highlight,which is not possessed by the other CV control charts in the past.In Chapter 5,in order to further improve the performance of the CV control chart and shorten the time to signal,the new HCVT control chart is proposed based on HWMA model and transformation method.Based on the HCVT chart,the VSSI HCVT control chart with variable sample size and sampling interval is designed,which fills the research gap of VSSI memory-type CV control chart.The outstanding advantage of this dynamic CV model is that its control limits and warning limits are not affected by the parameterγ₀and sample size n,that is,the errors of the parameter variation and estimation may be ignored.Additionally,the sensitivity of the HCVT and VSSI HCVT charts increases with the decrease of smoothing constantωor the increase of sample size n.Therefore,the HCVT and VSSI HCVT control charts are worthy of promotion.In Chapter 6,in case of multivariate process,based on the advanced homo-geneously weighted moving average model and the accurately derived calculation formula of the mean and variance of the multivariate sample CV,the HWMA-MCV chart is constructed.This chart is memory-type and improves the sensitivity of de-tecting the small and medium shifts of the MCV.The performances of HWMA-MCV are analyzed and compared with other MCV control charts.It is found that the overall performances of this control chart are the best.In Chapter 7,the MCV control chart with variable sampling interval is proposed,which is the pioneers of the research of the memory-type multivariate VSI control chart in this field.The simulation calculation program of the warning limit constant is provided.Based on the numerical results of average time to signal and standard deviation of the time to signal,the performance of the proposed chart is the best compared with the previous Shewhart-type charts with VSI for monitoring the MCV.The VSI HWMA-MCV chart provides a new and efficient method.In Chapter 8,the concluding remarks are given.Some unsolved problems and development directions of control chart for monitoring the CV are proposed.Fur-thermore,the prospects of the further study are given.