Abstract

We discuss issues related to the use of the normality assumption in statistical process monitoring with continuous data. Our illustrations involve the Shewhart X-chart. We illustrate some of the dangers and pitfalls in using nonlinear transformations in order to obtain the approximate normality of the process data. We argue that such transformations should rarely be made and never made prior to assessing and establishing process stability through the use of control charts and, if necessary, process improvements. The nonlinear transformation process can mask outliers, the importance of which need to be assessed by the process engineers or other domain experts. For clearly non-normal in-control processes, we recommend the use of an appropriate fitted distribution to obtain control limits in the ongoing monitoring of Phase II or the use of nonparametric control charts. We show that the low power of goodness-of-fit tests of normality can lead to an unexpectedly poor in-control statistical performance in Phase II when the assumption of normality is made incorrectly.

摘要

我们讨论了与在连续数据的统计过程监控中使用正态性假设相关的问题。我们的插图涉及休哈特X-图表。我们说明了使用非线性变换以获得过程数据的近似正态性的一些危险和陷阱。我们认为，在通过使用控制图评估和建立过程稳定性之前，应该很少进行这样的转换，并且在必要时，也不要进行过程改进。非线性转换过程可以掩盖异常值，其重要性需要由过程工程师或其他领域专家评估。对于明显非正态的受控过程，我们建议使用适当的拟合分布来获得对阶段 II 的持续监控或使用非参数控制图的控制限。