This paper studies control charts based on the BerG (which is a sum of Bernoulli and geometric random variables) process to deal with the cases of equidispersion, overdispersion, underdispersion, or zero inflation (or deflation). Its probability distribution function can be expressed in terms of the mean parameter and its cumulative distribution has a closed form, thus the construction of an $\overline{X}$ control chart to monitor the mean can be made easily. Additionally, we call attention that the asymptotic control limits for $\overline{X}$ control chart by central limit theorem (CLT) may lead to a serious erroneous decision. We present guidelines for practitioners about the minimum sample size needed to match out‐of‐control average run length (ARL₁) with the exact and asymptotic control limits in function of the shape parameter after an extensive simulation study. The proposed schemes are applied to monitoring the BerG mean parameter.

中文翻译：

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简单实用的统计控制图，用于监控计数数据

本文研究了基于BerG（伯努利和几何随机变量的总和）过程的控制图，以处理等距分散，过度分散，欠分散或零膨胀（或通缩）的情况。它的概率分布函数可以用均值参数表示，其累积分布具有封闭形式，因此可以构造一个$\overline{X}$控制图可以很容易地监控平均值。此外，我们需要注意的是，渐近控制极限为$\overline{X}$中心极限定理（CLT）得出的控制图可能会导致严重的错误决策。在广泛的模拟研究之后，我们为从业人员提供有关使失控平均游程长度（A R L ₁）与形状参数的精确且渐近控制极限相匹配所需的最小样本量的准则。所提出的方案被应用于监测BerG均值参数。