This paper presents the Bayesian EWMA control chart under two different loss functions (i) squared error loss function (SELF) and (ii) linex loss function (LLF) in the presence of measurement error (ME). We take posterior and posterior predictive distribution under the conjugate prior. We used a linear covariate model in the existence of ME to evaluate the control chart. We also studied the effects of multiple measurements and linear increasing variance methods in the existence of the ME. The average run length and standard deviation of run length are used to measure the performance of the Bayesian EWMA control chart with ME. We conducted the Monte Carlo simulation study to evaluate the performance of Bayesian EWMA control chart with ME. A real-life data example is also presented to demonstrate the application of the control chart.

中文翻译：

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不同损失函数下测量误差的贝叶斯 EWMA 控制图

本文介绍了存在测量误差 (ME) 的两种不同损失函数 (i) 平方误差损失函数 (SELF) 和 (ii) 线性损失函数 (LLF) 下的贝叶斯 EWMA 控制图。我们在共轭先验下采用后验和后验预测分布。我们在 ME 存在的情况下使用线性协变量模型来评估控制图。我们还研究了多重测量和线性增加方差方法在 ME 存在下的影响。使用平均游程长度和游程长度的标准偏差来衡量贝叶斯 EWMA 控制图与 ME 的性能。我们进行了蒙特卡罗模拟研究，以评估贝叶斯 EWMA 控制图与 ME 的性能。还提供了一个真实的数据示例来演示控制图的应用。