Control Charts and the Efficient Allocation of Sampling Resources
Control Charts and the Efficient Allocation of Sampling Resources
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DOI：
10.1198/004017004000000257
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发表时间：
2004-05
期刊：
影响因子：
2.5
通讯作者：
M. R. Reynolds;Z. G. Stoumbos
中科院分区：
文献类型：
--
作者：
M. R. Reynolds;Z. G. Stoumbos
用于监控过程平均值 μ 和过程标准差 σ 的控制图通常基于 n > 1 个观测值的样本，但在许多应用中使用单独观测值 (n = 1)。在本文中，我们从统计性能的角度研究了使用 n = 1 或 n > 1 是否更好的问题。我们假设单位时间观测数的采样率是固定的，因此使用 n = 1 意味着可以比 n > 1 时更频繁地采样。n 的最佳选择取决于所使用的控制图的类型，因此我们考虑休哈特图、指数加权移动平均值 (EWMA) 和累积和 (CUSUM) 图。对于每种类型的控制图，我们研究两个图表的组合，一个图表设计用于监控 μ，另一个图表设计用于监控 σ。文献中的大多数控制图比较都假设特殊原因会导致过程参数发生持续变化，这种变化一直持续到检测到变化为止。我们还考虑过程参数的瞬态变化（持续时间很短），以及参数以恒定速率偏离其控制值的漂移。我们使用各种类型的过程变化的预期检测时间和二次损失函数来评估控制图组合。当生成信号时，了解哪些参数发生了变化非常重要，因此还评估了控制图组合正确指示参数变化类型的能力。我们的总体结论是，最好采用 n = 1 个观测值的样本并使用 EWMA 或 CUSUM 图表组合。具有最佳整体性能的 Shewhart 图组合基于 n > 1，但该组合在几乎所有性能特征上都逊色于 EWMA 和 CUSUM 图组合（简单性除外）。这一结论似乎与关于 EWMA 和 CUSUM 图相对于 Shewhart 图的一些优点和缺点的传统观点相矛盾。
Control charts for monitoring the process mean μ and process standard deviation σ are often based on samples of n > 1 observations, but in many applications individual observations are used (n = 1). In this article we investigate the question of whether it is better, from the perspective of statistical performance, to use n = 1 or n > 1. We assume that the sampling rate in terms of the number of observations per unit time is fixed, so using n = 1 means that samples can be taken more frequently than when n > 1. The best choice for n depends on the type of control chart being used, so we consider Shewhart, exponentially weighted moving average (EWMA), and cumulative sum (CUSUM) charts. For each type of control chart we investigate a combination of two charts, one chart designed to monitor μ and the other designed to monitor σ. Most control chart comparisons in the literature assume that a special cause produces a sustained shift in a process parameter that lasts until the shift is detected. We also consider transient shifts in process parameters, which are of a short duration, and drifts in which a parameter moves away from its in-control value at a constant rate. We evaluate control chart combinations using the expected detection time for the various types of process changes and a quadratic loss function. When a signal is generated, it is important to know which parameters have changed, so the ability of control chart combinations to correctly indicate the type of parameter change is also evaluated. Our overall conclusion is that it is best to take samples of n = 1 observations and use an EWMA or CUSUM chart combination. The Shewhart chart combination with the best overall performance is based on n > 1, but this combination is inferior to the EWMA and CUSUM chart combinations on almost all performance characteristics (the exception being simplicity). This conclusion seems to contradict the conventional wisdom about some of the advantages and disadvantages of EWMA and CUSUM charts relative to Shewhart charts.