| Statistical process control is a quality management tool that monitors and improves the production process through the collection,analysis,and control of process data.In the production process,control charts are an important method for real-time monitoring of product quality.They can be used to analyze and judge whether the process is in a stable state.They are charts with control limits and have the function of distinguishing between normal and abnormal fluctuations.They are now widely used in financial forecasting,human flow trends,and other aspects Traditional quality control charts include Shewhart control charts,Exponential Weighted Moving Average(EWMA)control charts,and Cumulative Sum(CUSUM)control charts.Pareto distribution is a widely used probability distribution in practical production and quality management,known as the 80-20 rule.80% of problems are often caused by 20% of reasons It has been widely applied in reflecting quality issues and demonstrating quality improvement projects,and has now expanded to fields such as economics,finance,physics,ecology,etc.Its characteristic is that a small proportion accounts for the majority of the results,and its distribution of location and scale parameters can reflect the quality characteristics of the production process.Therefore,monitoring the changes in its parameters is of great significance.This article first proposes an EWMA control chart for monitoring the shape and scale parameters of the Pareto distribution separately based on the maximum likelihood estimation of the Pareto distribution parameters through inverse normal transformation,and compares and analyzes the performance of the control chart Secondly,two methods for monitoring both shape and scale parameters in a comprehensive control chart were presented Firstly,the Max-EWMA type control chart is constructed by taking the maximum value of two EWMA statistics Secondly,by using likelihood ratio test and combining with EWMA method,an ELR control chart is constructed The performance of two control charts with different sample sizes and smooth parameters was compared in terms of average running length under zero state and steady-state conditions The simulation results show that the new method proposed in this paper can effectively monitor the changes in the shape and scale parameters of the Pareto distribution,whether it is monitoring a single parameter control chart or monitoring a comprehensive control chart of two parameters simultaneously The article concludes with a simulation example to illustrate the practical application of the proposed method. |
