In many applications, the Poisson count data with varying sample sizes are monitored using statistical process control charts. Among these applications, the weighted CUSUM charts are developed to deal with the effect of the varying sample sizes. However, some of them use limited information of the sample size or the count data while assigning the weights. To gain more information of the process, the self-information weight functions are developed based on both the sample size and the observed count data. Then, the weighted CUSUM charts are proposed with the self-information-based weight. Simulation studies show the self-information-based weighted CUSUM charts perform better than the benchmark methods in detecting small shifts. Moreover, the performance of proposed method with estimated parameters is investigated via simulation. Finally, an example is given to illustrate the application of the proposed weighted CUSUM charts.

中文翻译：

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基于自我信息的加权 CUSUM 图表，用于监测不同样本量的泊松计数数据

在许多应用中，使用统计过程控制图监测具有不同样本量的泊松计数数据。在这些应用程序中，开发了加权 CUSUM 图表来处理不同样本量的影响。然而，其中一些在分配权重时使用样本大小或计数数据的有限信息。为了获得更多的过程信息，基于样本大小和观察到的计数数据开发了自信息权重函数。然后，使用基于自我信息的权重提出加权 CUSUM 图。模拟研究表明，基于自我信息的加权 CUSUM 图表在检测小偏移方面的性能优于基准方法。此外，通过仿真研究了具有估计参数的所提出方法的性能。最后，