An adaptive Shiryaev-Roberts procedure for monitoring dispersion
An adaptive Shiryaev-Roberts procedure for monitoring dispersion
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DOI：
10.1016/j.cie.2011.07.006
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发表时间：
2011-11
期刊：
影响因子：
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通讯作者：
Jiujun Zhang;Changliang Zou;Zhaojun Wang
中科院分区：
文献类型：
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作者：
Jiujun Zhang;Changliang Zou;Zhaojun Wang
在本文中，对 Shiryaev-Roberts (SR) 过程进行了检查，并将其与变点 CUSUM (CPC) 过程进行了比较，以监测正常过程的离散度。结果表明，对于预先指定的色散位移，SR 图的表现优于 CPC 图。实际上，当未来色散偏移的幅度未知时，总是希望设计一个控制图，使其在一系列偏移上表现得相当好，而不是在检测特定偏移水平时优化性能。与基于预先指定的色散位移的 SR 相比，本文提出了一种自适应 SR (ASR) 图，它不断调整其形式，以有效地表示平滑指数加权移动平均 (EWMA) 统计量偏离其目标值的情况。它可以很容易地实现，并且数值结果表明它可以平衡各种轮班规模的保护。
In this paper, the Shiryaev-Roberts (SR) procedure is examined and compared with the change point CUSUM (CPC) procedure for monitoring the dispersion of a normal process. It will be shown that the SR chart performs better than the CPC chart for the pre-specified dispersion shift. In practice, when the magnitude of a future dispersion shift is unknown, it is always desired to design a control chart to perform reasonably well over a range of shifts rather than to optimize the performance at detecting a particular level of shifts. Compared with SR based on a pre-specified dispersion shift, an adaptive SR (ASR) chart that continually adjusts its form to be efficient for signaling a smoothing exponentially weighted moving average (EWMA) statistic in deviation from its target value is proposed in this paper. It can be easily implemented and numerical results show that it balances protection against a broad range of shift sizes.