关键词: 统计过程控制, 联合监控, 非参数, 可变抽样区间

Abstract: Control charts play an important role in statistical process control and are widely used for process quality control in production and services. They are usually based on the premise that the process distribution is known and the parameters of the process distribution are used to construct the monitoring graph, which is referred to as a parametric control chart. Parametric control charts are suitable for mass production processes with more historical data, but due to fierce competition in the market and diverse customer demands, the modern production model has gradually turned from mass production to multi-species small-lot production. In the small-lot production mode, due to the lack of sufficient historical data to accurately infer the process distribution, it is often difficult for the traditional control chart method to play an effective role. Therefore, when the process distribution cannot be certain, non-parametric control charts are often considered, which have become a research hotspot in the field of process quality control for the advantage of not requiring known process distribution.
In the current study, there are more non-parametric control charts that monitor location or scale parameters individually, while there are fewer ones that monitor them jointly, and there is room to improve the monitoring efficiency. In practice, it is often difficult to determine in advance whether the location parameter or the scale parameter will change abnormally, and it may even be possible that both of them will shift at the same time, so it is very necessary to monitor both of them at the same time. In order to effectively monitor different degrees of abnormal shift in location and scale parameters in the case of unknown process distribution, a non-parametric dynamic exponentially weighted moving average (EWMA) control chart with Lepage type statistical form, abbreviated as DELPT (Dynamic EWMA of Lepage T²) chart, for joint monitoring of location and scale parameters, is constructed by Wilcoxon rank sum statistics and LOG statistics. The process of a larger shift in the process is usually easier to be recognized by the various types of control charts, but in the monitoring of smaller process shifts in the efficiency of the control charts, there is a large difference, so this paper uses a variable sampling interval (VSI) design to strengthen the effectiveness of the monitoring of small shifts. Secondly, in order to examine the influence of control chart parameters on monitoring efficiency, this paper analyzes the sensitivity of various parameters to monitoring efficiency by using Monte Carlo simulation. Since the sampling interval is not fixed, it is no longer appropriate to evaluate the performance by the conventional average run length (ARL), so the average single to time (ATS) is used to measure the control chart performance. Through 50,000 simulations, the appropriate value ranges of the control chart parameters are given in the paper for practical use, taking into account the efficiency and practicality. Then, the steps of using DELPT control charts are introduced through a real case study of the can encapsulation process, using the weight of the can as the key quality indicator to be monitored, and compared with the traditional control charts, DELPT charts indeed improve the monitoring efficiency and have better robustness. Finally, in order to further measure the monitoring efficiency of the nonparametric DELPT chart proposed in this paper, a comparative analysis of several other existing nonparametric control charts is carried out under symmetric and asymmetric distribution types. The optimal control charts under different shifts are also given, and the study shows that the control chart method proposed in this paper has a better monitoring performance for small and medium shifts in both location and scale parameters.
In summary, when the small number of controlled samples makes it difficult to accurately infer the process distribution statistically and when there is a possibility of simultaneous changes in the location and scale parameters, the use of non-parametric DELPT chart is a better way to monitor the quality. Because the nonparametric DELPT chart in this paper combines the idea of dynamics with that of memory control charts, it has good monitoring performance for small and medium shifts.

Key words: statistical process control, joint monitoring, nonparametric, variable sampling interval