The traditional process monitoring techniques used to study high-quality processes have several demerits, that is, high-false alarm rate and poor detection, etc. A recent and promising idea to monitor such processes is the use of time-between-events (TBE) control charts. However, the available TBE control charts have been developed in a nonadaptive fashion assuming the Poisson process. There are many situations where we need adaptive monitoring, for example, health, flood, food, system, or terrorist surveillance. Therefore, the existing control charts are not useful, especially in sequential monitoring. This article introduces new adaptive TBE control charts for high-quality processes based on the nonhomogeneous Poisson process by assuming the power law intensity. In particular, probability control limits are used to develop control charts. The proposed methodology allows us to get control limits that are dynamic and suitable for online process monitoring with an additional advantage to monitor a process where we believe the underlying failure rate may be changing over time. The average run length and coefficient of variation of the run length distribution are used to assess the performance of the proposed control charts. Besides simulation studies, we also discuss three examples to highlight the application of the proposed charts.

中文翻译：

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使用具有幂律强度的非齐次 Poisson 过程进行事件间时间监测

用于研究高质量过程的传统过程监控技术有几个缺点，即高误报率和较差的检测能力等。 监控此类过程的最新且有前途的想法是使用事件间隔时间（TBE ) 控制图。然而，可用的 TBE 控制图是在假设泊松过程的情况下以非自适应方式开发的。在很多情况下我们都需要自适应监控，例如健康、洪水、食品、系统或恐怖分子监控。因此，现有的控制图是没有用的，特别是在顺序监控中。本文通过假设幂律强度，介绍了基于非齐次 Poisson 过程的高质量过程的新自适应 TBE 控制图。特别是，概率控制限用于开发控制图。所提出的方法使我们能够获得动态且适合在线过程监控的控制限制，并具有额外的优势来监控我们认为潜在故障率可能随时间变化的过程。平均游程长度和游程长度分布的变异系数用于评估建议控制图的性能。除了模拟研究，我们还讨论了三个例子来强调所提出的图表的应用。平均运行长度和运行长度分布的变异系数用于评估建议控制图的性能。除了模拟研究，我们还讨论了三个例子来强调所提出的图表的应用。平均游程长度和游程长度分布的变异系数用于评估建议控制图的性能。除了模拟研究，我们还讨论了三个例子来强调所提出的图表的应用。