Design Of Improved Exponentially Weighted Moving Average T Control Chart

Since the 21 st century,with the increasingly prominent position of product quality in the core competitiveness of products,how to control and improve product quality has become the focus of more and more enterprises.As one of the powerful tools of statistical quality management,control chart can effectively improve product quality through real-time monitoring of production process,which is favored by scholars and enterprise product quality regulators.Among the common control charts,the Shewhart control chart is the most widely used,but it only uses the current sample information,it surely has weak detection ability for small or medium shift.In some modern precision manufacturing industries,such as semiconductor manufacturing,the Shewhart control chart obviously cannot meet the needs of detecting small shift of product quality characteristics in the production process.To solve this problem,this paper selects exponentially weighted moving average(EWMA)control charts for research,which has high sensitivity to small or medium shift.In addition,as consumers’ demand for personalized products increases day by day,more and more enterprises tend to use small bath production.The traditional control chart is often aimed at enterprises with mass production of products.At this time,there are enough sample data to accurately estimate the process mean and variance.In the small batch production mode,the sample size is often limited,which will lead to inaccurate estimation of the overall variance of the process.At this time,the performance of the traditional control chart will deteriorate and the detection effect will be unsatisfactory.In order to solve this problem,a control chart based on t statistics is proposed,which has good robustness when the process variance is unknown.In view of the superiority of EWMA control chart and t control chart,EWMA t control chart is worthy of study.In this paper,the performance of EWMA t control chart is improved.Firstly,in the actual production process,the direction of mean shift in some processes is usually predictable.At this point,the traditional two-sided EWMA t control chart monitoring process does not use the direction information of process mean shift.Therefore,in order to make full use of this information,the sensitivity of the traditional two-sided EWMA t control chart to the small shift of the monitoring process is improved.Based on the traditional EWMA t control chart,a one-sided EWMA t control chart is proposed to monitor the mean value of the process by using the information of the overall mean deviation direction of the process.The average run length(ARL)index of the control chart is obtained by Markov chain method.The optimal decision variables and optimal performance of the one-sided EWMA t control chart are analyzed under different sample sizes and mean deviation conditions.The statistical performance of the proposed control chart is compared with the traditional two-sided EWMA t control chart by simulation,which shows the superiority of the proposed one-sided EWMA t control chart.Secondly,the fixed sampling interval(FSI)scheme is used in the one-sided EWMA t control chart.In this scheme,the sampling interval between two continuous samples is fixed,and in the actual production process,the control chart with variable sampling interval scheme(VSI)is more sensitive in detecting the mean change of the process.Therefore,this paper proposes a one-sided EWMA t control chart with variable sampling interval characteristics.Average time to signal(ATS)and average number of samples to signal(ANSS)are derived by using Markov chain,and the simulation results show that the proposed VSI one-sided EWMA t control chart is better than the corresponding FSI control chart.Finally,based on the one-sided EWMA t control chart,a new one-sided EWMA(New EWMA,NEWMA)t control chart is proposed to monitor the process mean value.The control chart is composed of upper-sided EWMAt control charts and lower-sided EWMA t control charts.Monte Carlo simulation is used to simulate the run length(RL)performance of the control chart,the statistical performance of the control chart,the one-sided EWMAt control chart and the t control chart with several operation rules are compared,respectively,to verify the superiority of the proposed control chart performance.On the basis of the control chart,a VSI NEWMA t control chart is also proposed.