The Shewhart‐type exponential control chart is a popular and extensively used among all time‐between‐events control charts for its simplicity. When the parameter is unknown, Phase II control limits are constructed, and the success of its implementation depends to an extent on the estimated value of the parameter, obtained from Phase I dataset. However, when the Phase I data are contaminated with spurious observations/outliers, the performance of the chart is suspected to deviate from what is normally expected. Traditionally, maximum likelihood estimator (MLE) and minimum variance unbiased estimator (MVUE) are used to estimate the unknown process parameter. Both of estimators are the functions of sample mean. In this paper, the median‐based estimator (MBE) that is a function of sample median is used to construct Phase II control limits. Moreover, performance of the proposed chart is examined when Phase I sample consists of contaminated observations/outliers. It is found that the proposed chart outperforms the existing charts whether the sample is contaminated or not.

中文翻译：

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使用基于中位数的估计量来构建II期指数图

Shewhart型指数控制图由于其简单性而在所有事件之间的时间控制图中广受欢迎并广泛使用。当参数未知时，将构造阶段II控制极限，其实施成功与否在一定程度上取决于从阶段I数据集获得的参数估计值。但是，当第一阶段的数据被虚假的观察值/离群值污染时，图表的性能可能会偏离正常预期。传统上，最大似然估计器（MLE）和最小方差无偏估计器（MVUE）用于估计未知过程参数。这两个估计量都是样本均值的函数。在本文中，基于中位数的估计量（MBE）是样本中位数的函数，用于构建II期控制限值。此外，当阶段I样本包含受污染的观测值/异常值时，将检查建议图表的性能。可以发现，无论样品是否受到污染，建议的图表均优于现有图表。