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Optimal monitoring of Poisson data with known and unknown shifts
Computers & Industrial Engineering ( IF 7.9 ) Pub Date : 2021-01-09 , DOI: 10.1016/j.cie.2021.107100
Junjie Wang , Zhi Lin Chong , Peihua Qiu

The number of event occurrences, called counts are prevalent in many fields such as manufacturing industry and public health. Control charts have been widely employed to monitor such count data for quality improvement of products or medical service by assuming the data follows the Poisson distribution. However, the shift information of Poisson mean has not been well considered in current design of the exponentially weighted moving average (EWMA) control chart. This article studies the optimal design of the Poisson EWMA chart with known and unknown shift sizes integrated respectively in order to bridge the research gap. We simplify these two optimization problems to searching for a unique smoothing parameter in minimizing the out-of-control (OC) average run length (ARL) and OC expected ARL (EARL) over random shifts respectively. Due to the intractability of obtaining a closed-form solution, the Fibonacci search algorithm is proposed to find out the optimal smoothing parameter in a short time. The satisfactory performance of proposed optimal design method is demonstrated by numerous simulation results and two real datasets from manufacturing industry and public health.



中文翻译:

具有已知和未知偏移的泊松数据的最佳监视

事件发生的数量(称为计数)在制造业和公共卫生等许​​多领域都很普遍。通过假设数据遵循泊松分布,控制图已广泛用于监视此类计数数据,以提高产品或医疗服务的质量。但是,在当前的指数加权移动平均值(EWMA)控制图设计中,没有很好地考虑泊松均值的偏移信息。本文研究了已知和未知移位大小分别集成的Poisson EWMA图的最佳设计,以弥合研究差距。我们将这两个优化问题简化为寻找唯一的平滑参数,以分别最小化随机移位上的失控(OC)平均游程长度(ARL)和OC预期ARL(EARL)。由于获得封闭形式解的难处理性,提出了斐波那契搜索算法以在短时间内找出最优的平滑参数。大量的仿真结果以及来自制造业和公共卫生的两个真实数据集证明了所提出的最佳设计方法的令人满意的性能。

更新日期:2021-01-22
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