In the chemical and biochemical industries, batch processes play an important role in producing high-quality and value-added specialty products. The variables measured in such processes often have periodic trajectories with varying batch duration and fixed operational stages. The measured value of a process variable provides only part of the information about process conditions, while the process monitoring and operation activities mostly rely on the trends and trajectories of these variables. It is necessary to construct a trend-monitoring statistic to detect an abnormality in a batch process variable trajectory to provide operation decision support and guarantee product quality. In this paper, a new trend cumulative sum (CUSUM) chart is introduced as a way to detect the deviation of batch process variable trends, which may be caused by abnormal operations. This method relies on the extraction of variable trend features as a combination of derivatives through a functional description of variable trajectories. This then leads to the construction of an individual trend CUSUM chart and a multiple-trend CUSUM chart. The multiple-trend CUSUM chart, the sum of the trend CUSUM charts of all process variables, aims to improve the monitoring efficiency by combining the trend deviations of all variables in a single chart. The potential of these novel univariate control charts is demonstrated using the batch manufacture of polypropylene (PP). When several simulated and actual batches are studied, the results show that the trend CUSUM chart is capable of capturing trend abnormalities. We also show, by comparison, that alarms can be triggered in the trend CUSUM chart before the measured process variables exceed the control limits of their Shewhart individuals charts, allowing for the corrections to be made at an early stage of an abnormal situation.

中文翻译：

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制定新的趋势累积总和图以监视批生产过程变量

在化学和生化工业中，批处理过程在生产高质量和高附加值的特种产品中起着重要作用。在此类过程中测得的变量通常具有周期性轨迹，这些轨迹具有变化的批处理持续时间和固定的操作阶段。过程变量的测量值仅提供有关过程条件的部分信息，而过程监视和操作活动主要取决于这些变量的趋势和轨迹。有必要构建趋势监视统计信息以检测批处理过程变量轨迹中的异常情况，以提供操作决策支持并保证产品质量。本文中的新趋势累计总和（CUSUM）图表引入了一种检测批处理过程变量趋势偏差的方法，该偏差可能是由异常操作引起的。这种方法依赖于通过可变轨迹的功能描述将可变趋势特征提取为导数的组合。然后，这将导致构建单个趋势CUSUM图表和多趋势CUSUM图表。多趋势CUSUM图表是所有过程变量的趋势CUSUM图表的总和，旨在通过在单个图表中组合所有变量的趋势偏差来提高监视效率。这些新颖的单变量的潜力使用聚丙烯（PP）的批量生产演示了控制图。当研究几个模拟批次和实际批次时，结果表明趋势CUSUM图表能够捕获趋势异常。通过比较，我们还表明，可以在趋势CUSUM图表中触发警报，然后再测量的过程变量超过其Shewhart个人图表的控制极限，从而可以在异常情况的早期进行更正。