关键词: 统计过程控制, 联合监控, 马尔科夫链, 多目标优化

Abstract: Statistical process control can use the principle of mathematical statistics to ensure the smooth operation of the production process of the enterprise and make sure that the quantity, quality, cost and time required for production meet the requirements of the conditions, so that the enterprise forms a competitive production management ability. This has been widely concerned. As one of the most widely used product quality control tools for statistical process control, control chart is widely used by various enterprises. The existing control chart in this paper is optimized and improved. By combining the conventional Shewhart chart with the exponential weighted moving average (EWMA) control chart and introducing the idea of dynamic control chart, a VSET control chart for jointly monitoring position and scale parameters is established by constructing Chi-square distribution statistics to meet the needs of enterprises for more efficient joint monitoring.
In this paper, the average product length (APL) and the average product quality cost per unit are taken as the statistical and economic evaluation indexes of the control chart, and the calculation methods of the two indexes are analyzed based on Markov chain, and the multi-objective optimization design model of the economic statistics of the chart is established. In the MATLAB 2021 environment, NSGAⅢ (non-dominated sorting genetic algorithalgorithm-Ⅲ algorithm is used to solve the optimal dasign model, and the non-inferior solution set under the given production parameters and control parameters is obtained. Then, through the analysis of a numerical example, this paper shows how to apply the multi-objective optimization model of economic statistics of VSET control chart in the enterprise. Through the sensitivity analysis, the influence of the optimization model of the VSET control chart on the value of the objective functions and their relations are explained. Through the comparative analysis, the application range of the VSET control chart optimization model proposed in this paper is illustrated.
The research results of this paper show that the VEST control chart economic statistics multi-objective optimization model proposed in this paper can effectively monitor abnormal shifts occurring in position and scale parameters. Besides, compared with the partial combination control chart of this control chart from the aspects of statistics and economy, Shewhart chart, VSI EWMA chart and Shewhart-EWMA chart with variable sampling interval have good effects on abnormal deviation of different degrees of position and scale parameters, and have a wider application range, which can effectively improve the monitoring efficiency of control chart and reduce the quality loss and economic cost of quality monitoring for enterprises.
Finally, the paper also needs to look forward to the following aspects: the innovation of this paper lies in the establishment of Chi-square distribution statistics that can jointly monitor the position and scale parameters, and the combination monitoring of two commonly used control charts to improve the applicability of control charts. Whether the combination monitoring of the other two types of control charts can be more advantageous than monitoring alone needs further consideration. In addition, this paper only studies one type of dynamic control chart, which is the control chart with variable sampling interval. For dynamic control charts, there are also control charts with variable sample size and control charts with both variable sample size and sampling interval. How to apply these concepts of dynamic control charts to combined control charts and improve the monitoring efficiency of control charts still needs further research.

Key words: statistical process control, joint monitoring, Markov chain, multi-objective optimization