关于累积和图与序贯概率比检验有效性评价的注记
A Note on Efficient Performance Evaluation of the Cumulative Sum Chart and the Sequential Probability Ratio Test
摘要：
我们建立了一个简单的连接之间的某些控制特性的控制范围内的运行长度和他们的失控同行。这种联系是成对积分（更新）方程的形式。推导利用沃尔德的似然比的身份和众所周知的事实，即，图是相当于重复应用沃尔德的SPRT。考虑的特征包括整个游程分布和所有相应的时刻，从零状态ARL开始。我们的结果的一个特别的实际好处是，它使在控制和失控的特性的CNOUM运行长度被同时计算。此外，由于SPRT序列的等价性，SPRT在空值和替代值下的Oscillation和OC函数也可以同时计算。这将使人们可能选择设计来进行实际计算的任何数值方法的效率加倍。
英文摘要：
We establish a simple connection between certain in-control characteristics of the CUSUM Run Length and their out-of-control counterparts. The connection is in the form of paired integral (renewal) equations. The derivation exploits Wald's likelihood ratio identity and the well-known fact that the CUSUM chart is equivalent to repetitive application of Wald's SPRT. The characteristics considered include the entire Run Length distribution and all of the corresponding moments, starting from the zero-state ARL. A particular practical benefit of our result is that it enables the in- and out-of-control characteristics of the CUSUM Run Length to be computed concurrently. Moreover, due to the equivalence of the CUSUM chart to a sequence of SPRTs, the ASN and OC functions of an SPRT under the null and under the alternative can all be computed simultaneously as well. This would double up the efficiency of any numerical method one may choose to devise to carry out the actual computations.
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