Time between events (TBE) charts are used in high‐yield processes where the rate of occurrences is very low. In the current article, we propose a triple exponentially weighted moving average control chart to monitor TBE (regarded as triple exponentially weighted moving average TEWMA‐TBE chart) modeled by a gamma distribution. One‐ and two‐sided schemes of the proposed chart are designed and compared with the double EWMA DEWMA‐TBE and EWMA‐TBE charts. It is shown that the lower‐ and two‐sided TEWMA‐TBE charts outperform its competitors, especially for small to moderate downward shifts, while the upper‐sided TEWMA‐TBE chart has very good detection ability for small shifts. We also study the robustness of the proposed chart when the true distribution is a Weibull or a lognormal and it is found that the TEWMA‐TBE chart has better robustness properties than its competitors, especially for small shifts. Two illustrative examples from airplane accidents and earthquakes are also provided to display the application of the proposed chart.

中文翻译：

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用于监控事件之间时间的三重指数加权移动平均控制图

事件间隔时间（TBE）图表用于发生率非常低的高收益过程中。在当前的文章中，我们提出了一个三重指数加权移动平均控制图来监视以伽马分布为模型的TBE（被视为三重指数加权移动平均TEWMA-TBE图表）。设计了拟议图表的单边计划和双面计划，并将其与双EWMA DEWMA-TBE和EWMA-TBE图进行了比较。结果表明，下方和两侧的TEWMA-TBE图表均胜过其竞争对手，尤其是在小至中度的向下移位时，而上方的TEWMA-TBE图表对于小幅度的移位具有很好的检测能力。当真实分布为Weibull或对数正态时，我们还研究了拟议图表的鲁棒性，并且发现TEWMA-TBE图表具有比其竞争对手更好的鲁棒性，特别是对于小班次。还提供了两个来自飞机事故和地震的说明性示例，以显示建议的图表的应用。