Abstract

Statistical process control (SPC) charts provide a powerful tool for monitoring production lines in manufacturing industries. They are also used widely in other applications, such as sequential monitoring of internet traffic flows, disease incidences, health care systems, and more. In practice, quality/performance variables are often affected in a complex way by many covariates, such as material, labor, weather conditions, social/economic conditions, and so forth. Among all these covariates, some could be observed, some might be difficult to observe, and the others might even be difficult for us to notice their existence. Intuitively, an SPC chart could be improved by using helpful information in covariates. However, because of the complex relationship between the quality/performance variables and the covariates, shifts in the quality/performance variables could be due to certain covariates whose data cannot be collected. On the other hand, shifts in some observable covariates may not necessarily cause shifts in the quality/performance variables. Thus, it is challenging to properly use covariate information for process monitoring in a general setting. This article suggests a method to handle this problem. An effective exponentially weighted moving average chart is developed, in which its weighting parameter is chosen large if the related covariates included in the collected data tend to have a shift and small otherwise. Because the covariate information is used in the weighting parameter only, the chart is designed solely for detecting shifts in the quality/performance variables, but it can react to a future shift in the quality/performance variables quickly because the helpful covariate information has been used in its observation weighting mechanism. Extensive numerical studies show that this method is effective in many different cases.

摘要

统计过程控制 (SPC) 图表为监控制造行业的生产线提供了强大的工具。它们还广泛用于其他应用，例如对互联网流量、疾病发病率、医疗保健系统等的顺序监控。在实践中，质量/性能变量通常以复杂的方式受到许多协变量的影响，例如材料、劳动力、天气条件、社会/经济条件等。在所有这些协变量中，有的可以观察到，有的可能很难观察到，有的甚至可能我们很难注意到它们的存在。直观地说，可以通过在协变量中使用有用的信息来改进 SPC 图表。然而，由于质量/性能变量与协变量之间的复杂关系，质量/性能变量的变化可能是由于无法收集数据的某些协变量造成的。另一方面，一些可观察协变量的变化不一定会导致质量/性能变量的变化。因此，在一般环境中正确使用协变量信息进行过程监控是具有挑战性的。本文提出了一种处理此问题的方法。开发了一个有效的指数加权移动平均图，其中，如果收集的数据中包含的相关协变量倾向于具有偏移，则选择较大的加权参数，否则选择较小的加权参数。由于协变量信息仅用于权重参数，因此图表专为检测质量/性能变量的变化而设计，但它可以快速对质量/性能变量的未来变化做出反应，因为有用的协变量信息已被用于其观察加权机制。大量的数值研究表明，这种方法在许多不同的情况下都是有效的。