The Comparison Of Various EWMA Schemes For Monitoring Binomial Proportion

Control charts are an important tool in statistical process control,which can monitor fluctuations in the manufacturing process and have a wide range of applications in equipment maintenance,production decision-making,and pharmaceutical management.The traditional models of control charts include Shewhart control charts,cumulative sum(CUSUM)control charts,and exponentially weighted moving average(EWMA)control charts.The traditional Shewhart control chart performs well in monitoring large fluctuations,but the effect is not ideal in monitoring small fluctuations.CUSUM and EWMA charts can improve the monitoring effect during large fluctuations.During the production process,product quality can be measured by the number of defects or non-conforming products in n random samples.In order to improve the quality of products in the production process,it is necessary to monitor the unqualified rate of products.The number of nonconforming products is usually assumed to obey the binomial distribution with parameters n and p.Monitoring by using control charts.When the control chart sends an alarm signal,the producer should immediately stop the production process and check the possible causes of the alarm,in order to avoid significant economic losses.In order to detect changes in the rate of non-conforming products more quickly,many scholars have proposed methods for detecting the rate of non-conforming products,including EWMA control charts and CUSUM control charts.In recent years,the weighted likelihood ratio test(WLRT)based method has received widespread attention.This method achieves the goal of using all samples by assigning different weights to the likelihood ratio of the samples over time.By accumulating historical samples,the ability to detect processes is improved.In addition,this method is simple in design,easy to operate,and can handle single sample situations.In this article,we compare the performance of a class of EWMA control charts with a newly designed weighted EWMA control chart that can be known as the EWLRT chart based on the WLRT.These schemes are suitable for monitoring fraction non-conforming.Some directions for choosing optimal parameters based on the relative mean index(RMI)are given,and various competing schemes at the optimal level are considered.Current comparisons consider the zero-state run-length performance and the conditional expected delay(CED)for a delayed shift.The results show that the detection effect of EWLRT chart is better than its competitors in detecting small to moderate changes.Some properties of the EWLRT scheme are outlined,and a real example based on the jewellery manufacturing process is used to describe the implementation.