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Detection of linear trends in process mean

机译：检测过程均值的线性趋势

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摘要

In this paper, we develop a process control approach to detect linear trends in the process mean. A statistic based on the deviation between the target mean and the expected mean of the process is used in the development of the new approach. The statistic is shown to have a chi-square distribution. The approach is described and its performance is compared with cumulative sum (CUSUM), exponentially weighted moving average (EWMA), Shewhart, and generalized likelihood ratio (GLR) charts in detecting linear trends in the process mean. The results indicate that proposed approach is effective in detecting small to large trends. We also investigate the run length properties of the proposed approach under linear trends and compare its values with simulation results. Finally, we analyse the performance of the proposed approach in detecting the time when a drift occurs in the process and compare it with CUSUM and EWMA estimators. The results show that the proposed approach is more effective in detecting drift time for moderate and large trends.
机译：在本文中，我们开发了一种过程控制方法来检测过程均值中的线性趋势。在新方法的开发中，使用了基于过程的目标均值和预期均值之间的偏差的统计数据。该统计数据显示为具有卡方分布。描述了该方法，并将其性能与累积和（CUSUM），指数加权移动平均值（EWMA），Shewhart和广义似然比（GLR）图进行比较，以检测过程平均值的线性趋势。结果表明，所提出的方法可有效地检测从小到大的趋势。我们还研究了线性趋势下拟议方法的运行长度属性，并将其值与仿真结果进行了比较。最后，我们分析了该方法在检测过程中发生漂移的时间方面的性能，并将其与CUSUM和EWMA估计量进行了比较。结果表明，所提出的方法对于中度和大趋势的漂移时间检测更为有效。

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