CONTINUOUS INSPECTION SCHEMES
CONTINUOUS INSPECTION SCHEMES
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DOI：
10.1093/biomet/41.1-2.100
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发表时间：
1954-01-01
期刊：
影响因子：
2.7
通讯作者：
PAGE, ES
中科院分区：
文献类型：
--
作者：
PAGE, ES
当按顺序进行观测时，可能会发生将整个观测集划分为子集的情况，每个子集都可以视为来自共同分布的随机样本，每个子集对应于该分布的不同参数值。本文要考虑的问题是子样本的识别和参数值变化的检测。这类问题可能出现在许多应用领域。例如，在超感官知觉实验中，受试者对一系列问题给出的正确答案的比例可能在实验过程中发生变化，可能需要估计变化的位置，或者在注意到变化时停止实验。同样，在一个心理学实验中，一个受试者被要求猜测下一个随机抽取的球的颜色，从一个装有两种颜色的球的袋子中取出另一个球，受试者在使用同一袋球的一系列试验中正确猜测的比例可能会改变，因为他从先前的猜测结果中获得了一些关于袋子构成的知识；估计一下变化发生的时间点可能是有意义的。更广为人知的是在工业中出现的检测连续生产过程中产品质量变化的问题。有些这样的工序在相当长的时间内保持产出质量大致恒定；偶尔，可能是由于过程中的某个点的错误，质量恶化，输出的很大一部分变得不可接受。输出的质量可以通过一些可测量的特性来评估（例如，当文章的长度以恒定的方差正态分布时，平均长度可以用作质量的指示），或者通过输出不符合给定规格的部分来评估。一般情况下，可以为输出分配一个质量数，即可以作为分布的一个参数。我们感兴趣的是x的变化。检测分布的平均值变化的最简单的标准之一是最后几个观测值的加权和，即移动平均。如果_ _小，_ _大的变化将很快被检测到，但小的变化只能缓慢地检测到；另一方面，为了最好地检测到微小的变化，需要更大的值，但由于移动平均线阻尼了单个极端观测的影响，随后会注意到较大的变化。一般来说，基于移动平均线的规则的结果很难评估。Anscombe, Godwin & Plackett（1947）给出了一种这样的规则理论，用于从变化均值的二项总体中识别观测中的子样本。
Whenever observations are taken in order it can happen that the whole set of observations can be divided into subsets, each of which can be regarded as a random sample from a common distribution, each subset corresponding to a different parameter value of the distribution. The problems to be considered in this paper are concerned with the identification of the subsamples and the detection of the changes in the parameter value. Such problems can arise in a number of fields of application. For example, in an experiment in extrasensory perception the proportion of correct answers given by a subject in response to a series of questions may change during the course of the experiment, and it may be desired to estimate the position of the change or to stop the experiment when a change is noticed. Again, in a psychological experiment in which a subject is required to guess the colour of the next ball to be drawn at random with replacement from a bag containing balls of two colours the subject's proportion of correct guesses in a series of trials with the same bag of balls may change as he gains some knowledge of the constitution of the bag from the results of earlier guesses; it may be of interest to estimate the point at which the change took place. More widely known are the occurrences in industry of problems of detecting changes in the quality of the output from a continuous production process. Some such processes maintain an approximately constant quality of output for considerable periods; occasionally, probably because of a fault at some point of the process, the quality worsens and a large proportion of the output becomes unacceptable. The quality of the output may be assessed by some measurable characteristic (eg when the length of articles is normally distributed with constant variance the mean length may be used as an indication of quality), or by the fraction of the output that fails to meet given specifications. In general, it will be possible to assign a quality number, в, to the output which may be taken as a parameter of the distribution. We are interested in the changes in в. One of the simplest criteria for detecting a change in the mean, в, of the distribution is a weighted sum of the last few, к say, observations, ie a moving average. If к is small, large changes in в will be detected rapidly but small changes only slowly; on the other hand, a larger value of к will be required for the best detection of small changes in в but then large changes will be noticed later owing to the moving average damping the effect of a single extreme observation. In general, the consequences of rules based on moving averages are difficult to evaluate. The theory of one such rule for identifying the subsamples in observations from a binomial population of changing mean has been given by Anscombe, Godwin & Plackett (1947).