Abstract

Statistical Process Control (SPC) charts are widely used in manufacturing industry for monitoring the performance of sequential production processes over time. A common practice in using a control chart is to first collect samples and take measurements of certain quality variables from them at equally-spaced sampling times, and then make decisions about the process status by the chart based on the observed data. In some applications, however, the quality variables are associated with certain covariates, and it should improve the performance of an SPC chart if the covariate information can be used properly. Intuitively, if the covariate information indicates that the process under monitoring is likely to have a distributional shift soon based on the established relationship between the quality variables and the covariates, then it should benefit the process monitoring by collecting the next process observation sooner than usual. Motivated by this idea, we propose a general framework to design a variable-sampling control chart by using covariate information. Our proposed chart is self-starting and can well accommodate stationary short-range serial data correlation. It should be the first variable-sampling control chart in the literature that the sampling intervals are determined by the covariate information. Numerical studies show that the proposed method performs well in different cases considered.

摘要

统计过程控制 (SPC) 图表广泛用于制造业，用于监控连续生产过程随时间推移的性能。使用控制图的一种常见做法是首先收集样本并在等间隔的采样时间从它们中测量某些质量变量，然后根据观察到的数据通过控制图对过程状态做出决定。然而，在某些应用程序中，质量变量与某些协变量相关联，如果可以正确使用协变量信息，它应该会提高 SPC 图的性能。直观地说，如果协变量信息表明，基于已建立的质量变量和协变量之间的关系，受监控的过程可能很快就会发生分布变化，那么它应该通过比平时更快地收集下一个过程观察来有益于过程监控。受这个想法的启发，我们提出了一个通用框架来设计一个使用协变量信息的变量采样控制图。我们提出的图表是自启动的，可以很好地适应固定的短程串行数据相关性。抽样区间由协变量信息确定，应该是文献中第一个变量抽样控制图。数值研究表明，所提出的方法在考虑的不同情况下表现良好。我们提出的图表是自启动的，可以很好地适应固定的短程串行数据相关性。抽样区间由协变量信息确定，应该是文献中第一个变量抽样控制图。数值研究表明，所提出的方法在考虑的不同情况下表现良好。我们提出的图表是自启动的，可以很好地适应固定的短程串行数据相关性。抽样区间由协变量信息确定，应该是文献中第一个变量抽样控制图。数值研究表明，所提出的方法在考虑的不同情况下表现良好。