Self‐Starting Cusum Charts for Location and Scale
Self‐Starting Cusum Charts for Location and Scale
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DOI：
10.2307/2348827
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发表时间：
1987-10
期刊：
影响因子：
--
通讯作者：
D. Hawkins
中科院分区：
文献类型：
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作者：
D. Hawkins
在某些质量控制问题中，不知道精确的过程平均值和标准偏差在控制之下，但希望确定是否存在与过程启动时获得的条件的偏差。这种情况并没有很好地涵盖了标准的累积和程序，它通常假设已知的工艺参数。本文使用自启动以来对过程进行的所有观察的运行平均值和标准差作为过程平均值和标准差的未知真实值的替代品。利用残差独立性的一些理论性质，建立了两对累积和：一个检验过程的位置恒定性，另一个检验过程的传播恒定性。当过程处于控制之下时，这两个累计和对都是近似正常的N（O，1）量（因此是很好理解的），但是如果位置、散布或两者都改变，则非中心性被引入位置和尺度累计和对中的一个或两个，并且它漂移失控。它表明，该程序在检测过程中的变化表现良好，即使在比较经常乌托邦的情况下，在该过程中的均值和方差是已知的正是开始之前的累积和。如果要避免大量的寄生信号，则精确地说。虽然在讨论累积量时通常假设过程规范是确切已知的，但在许多情况下，它在某种程度上是不确定的，在这些条件下，已知均值和方差的假设是不合适的。作者特别感兴趣的一个案例是在化学实验室中控制分析的偏差和精度。一个很好的方法是使用参考资料（Mandel 1964）。参比物质是一批与实验室分析相同种类的物质（例如，从先前的托运货物中获得），其中部分物质与生产物质一起定期沿着分析。参比物质含量测定与其先前平均值或标准差的偏离表明偏倚或精密度发生变化。请注意，所需的控制仅针对参比物质所得值的任何变化。参比物质的真实含量（理想的目标工艺平均值）实际上是什么并不重要，质量控制系统不应基于对工艺平均值的准确了解的假设。这种不确定性呈现出
In some quality control problems, it is not known what the exact process mean and standard deviation are under control but it is desired to determine whether there have been drifts from the conditions obtained at the process start-up. This situation is not well-covered by standard cumulative sum procedures, which generally assume known process parameters. This paper uses the running mean and standard deviation of all observations made on the process since start-up as substitutes for the unknown true values of the process mean and standard deviation. Using some theoretical properties of independence of residuals, two pairs of cusums are set up: one testing for constancy of location of the process, and the other for constancy of the spread. While the process is under control, both these cusum pairs are of approximately normal N(O, 1) quantities (and therefore are well understood), but if the location, the spread or both change, then non-centrality is introduced into one or both of the location and scale cusum pairs, and it drifts out-of-control. It is shown that the procedure performs well in detecting changes in the process, even in comparison with the often utopian situation in which the process mean and variance are known exactly prior to the start of the cusum. precisely if large numbers of spurious signals are to be avoided. While it has usually been assumed in discussion of cusums that the process specification is known exactly, there are many circumstances in which it is to some extent uncertain, and under these conditions the assumption of known mean and variance is inappropriate. A case of particular interest to the author arises in the control of assaying in a chemical laboratory for bias and precision. A good way of doing this is (Mandel 1964) by using reference materials. A reference material is a batch of the same sort of material as is assayed in the laboratory (obtained for example from a previous consignment), portions of which are assayed regularly along with the production material. A depar- ture of the assays of the reference material from their previous mean or standard deviation indicates a change in bias or precision. Note that the control required is simply for any change in the values obtained for the reference material. It is immaterial what the true assay of the reference material (the ideal target process mean) actually is, and the quality control system should not be predicated on the assumption of an exact knowledge of the process mean. This indeterminancy presents