Research On Adaptive Exponentially Weighted Moving Average Control Chart

Since the 21 st century is the century of quality,the competition of enterprises boils down to product quality.Therefore,advanced quality control theories and methods have become a hot research topic in academia and industry.Control chart is among the most important and widely used tools in Statistical Process Monitoring(SPM),it combines rigorous time series analysis methods with graphical presentation of data,often yielding insights into the data more quickly and in a very opportune way to guarantee the quality of production.The traditional methodologies,such as Shewhart,CUSUM and EWMA control charts,involve optimization of a specific magnitude of the shift,but the shift size is rarely known accurately in practice.If the process experiences a shift with a totally different magnitude as the expected one,the efficiency of these control charts can be strongly affected.A suitable methodology called adaptive EWMA control chart,which combines the Shewhart and EWMA schemes in a smooth way,is proposed.This AEWMA scheme is proven to be superior to conventional schemes in achieving a good overall performance.The existing AEWMA control charts are usually designed with a known normal distribution assumption.However,on one hand,the actual distribution is different from the assumed one,and the existing of measurement error will produce more frequent false out-of-control signals.On the other hand,a specific parametric model and the known parameter assumption is usually violated and it leads to a deteriorated performance for control charts.Moreover,in order to improve the detection efficiency of the control chart,dynamic sampling strategies are gradually receiving attention.Therefore,we have updated the AEWMA control chart on several occasions considering the foregoing questions.The main research results of this paper are summarized as follows:(1)The design of AEWMA control chart with measurement error is investigated.Consid-ering in actual quality control applications,the control chart is a powerful tool but itsperformance is adversely affected by the contamination from either the inspector or themeasuring device leading to measurement errors or outliers.We investigate the perfor-mance of the AEWMA control chart with measurement errors,and a Markov methodol-ogy is proposed to obtain the optimal parameters by considering a linearly covariate errormodel.Comparisons with the EWMA control chart confirm the superiority of the AEW-MA control chart for detecting a wide range of shifts in the case of precise and imprecisedata.(2)The design of AEWMA control chart with estimated parameters is investigated.Consid-ering in actual quality control applications,there are many situations where the processparameters are unknown and need to be estimated from a very limited number of sam-ples.We develop an AEWMA control chart with estimated parameters to monitor themean value of a normal process.It is shown that the performance of the proposed AEW-MA control chart is seriously affected when parameters are estimated compared with theknown-parameter case,and it requires a large amount of Phase I data to reduce the vari-ation in the in-control ARL distribution up to a reasonable level.Therefore,a bootstrap-based design approach is applied here and,the performance of the AEWMA control chartis compared with that of the existing Shewhart and EWMA control charts.The compara-tive results show that the AEWMA control chart represents a good alternative to achievea reasonable balance for various shift sizes.(3)A new nonparametric AEWMA control chart is proposed.Considering in actual qualitycontrol applications,there are many situations where the underlying distribution is un-known.A new nonparametric AEWMA control chart for count data,based on the Signstatistic,is proposed without requiring any parametric probability distribution for the un-derlying process.It combines the advantages of a nonparametric control chart with thebest overall shift detection properties of an AEWMA-type control chart.An appropri-ate discrete-time Markov chain technique is provided to compute the exact run lengthproperties of the proposed chart without any expensive simulation or unreliable approxi-mation.Detailed guidelines and recommendations for selecting the chart parameters areprovided.An extensive comparative study demonstrates the superiority of this nonpara-metric AEWMA control chart over a number of existing control charts for detecting awide range of location shifts.(4)The design of the Variable Sampling Interval(VSI)AEWMA control chart is investigat-ed.To improve the detection performance of the Fixed Sampling Interval(FSI)AEWMAcontrol chart,we propose a new VSI AEWMA control chart.A Markov chain approachis used to evaluate the performance of the new VSI AEWMA control chart with two sam-pling intervals.And comparative results show that the proposed control chart performsbetter than the FSI AEWMA control chart and than other VSI EWMA and CUSUMcontrol charts over a wide range of shifts.