Abstract

In applications, most processes for quality control and management are multivariate. Thus, multivariate statistical process control (MSPC) is an important research problem and has been discussed extensively in the literature. Early MSPC research is based on the assumptions that process observations at different time points are independent and they have a parametric distribution (e.g., Gaussian) when the process is in-control (IC). Recent MSPC research has lifted the “parametric distribution” assumption, and some nonparametric MSPC charts have been developed. These nonparametric MSPC charts, however, often requires the “independent process observations” assumption, which is rarely valid in practice because serial data correlation is common in a time series data. In the literature, it has been well demonstrated that a control chart who ignores serial data correlation would be unreliable to use when such data correlation exists. So far, we have not found any existing nonparametric MSPC charts that can accommodate serial data correlation properly. In this paper, we suggest a flexible nonparametric MSPC chart which can accommodate stationary serial data correlation properly. Numerical studies show that it performs well in different cases.

摘要

在应用中，大多数质量控制和管理过程都是多元的。因此，多元统计过程控制 (MSPC) 是一个重要的研究问题，并在文献中进行了广泛的讨论。早期的 MSPC 研究基于这样的假设：不同时间点的过程观察是独立的，并且当过程处于受控状态 (IC) 时它们具有参数分布（例如，高斯分布）。最近的 MSPC 研究提升了“参数分布”假设，并开发了一些非参数 MSPC 图表。然而，这些非参数 MSPC 图表通常需要“独立过程观察”假设，这在实践中很少有效，因为序列数据相关性在时间序列数据中很常见。在文献中，已经很好地证明，当存在此类数据相关性时，忽略序列数据相关性的控制图将不可靠。到目前为止，我们还没有发现任何现有的非参数 MSPC 图可以适当地适应序列数据相关性。在本文中，我们提出了一种灵活的非参数 MSPC 图，它可以适当地适应平稳的序列数据相关性。数值研究表明它在不同情况下表现良好。