基于最大熵的轮廓控制图
Profile control chart based on maximum entropy
AI总结：
本文提出基于最大熵原理和线性回归的两种方法，利用T2 Hotelling统计量同时监控简单线性轮廓的截距与斜率，并通过仿真和半导体、制药实例验证最大熵方法在检测变化方面更具优势。
摘要：
在制造过程中，随时间监控过程对于减少资金和时间浪费非常重要。Shewhart、CUSUM和EWMA等控制图常用于监控具有单一目标属性的过程，这些控制图被用于具有不同偏移范围的各种过程。在某些情况下，过程质量由不同类型的轮廓来表征。本文的目的是监控轮廓系数而不是过程均值。本文提出了两种方法，用于同时监控简单线性轮廓的截距和斜率。在这方面，本文对两种方法进行了比较。第一种是线性回归，另一种是最大熵原理。使用T2 Hotelling统计量将两个系数转化为一个标量。通过仿真研究，从第二类错误和平均运行长度两方面对两种方法进行比较。最后，给出了两个实际例子来证明所提出的控制图的适用性。第一个例子涉及半导体，第二个例子涉及制药生产过程。两种方法的性能相对相似。在制药例子中，最大熵在正确识别差异方面发挥了重要作用，而线性回归未能正确检测到这些变化。
英文摘要：
Monitoring a process over time is so important in manufacturing processes to reduce the waste of money and time. Some charts as Shewhart, CUSUM, and EWMA are common to monitor a process with a single intended attribute which is used in different kinds of processes with various ranges of shifts. In some cases, the process quality is characterized by different types of profiles. The purpose of this article is to monitor profile coefficients instead of a process mean. In this paper, two methods are proposed for monitoring the intercept and slope of the simple linear profile, simultaneously. In this regard, two methods are compared here. The first one is the linear regression, and the one is the maximum entropy principle. The T2 Hotelling statistics is used to transfer two coefficients to a scalar. A simulation study is applied to compare the two methods in terms of the second type of error and average run length. Finally, two real examples are presented to demonstrate the applicability of the proposed chart. The first one is about semiconductors, and the second one is about pharmaceutical production processes. The performance of the methods is relatively similar. The maximum entropy plays an important role in correctly identifying differences in the pharmaceutical example, while linear regression did not correctly detect these changes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
