Average Run Length(ARL)に関する2,3の考察

抄録

In this paper, we discuss the statistical meaning and the usefulness of the average run length (ARL) through the consideration on the cumulative sum schemes and the runs rule schemes, of which behavior can be represented by Markov models. Observing the geometric approximation to the run length distribution (RLD), we conclude the following. Regarding the type I error, ARL is a useful measure which can give the representation of RLD, because ARL can be considered to be the only parameter of the geometric distribution. Furthermore, observing the conservativeness of the geometric approximation, we can find a different property between the two schemes on the relation between ARL and the probability of the type I error. Regarding the power of test, ARL has no meaning but the mean of RLD from the statistical viewpoint. In a practical representation, however, ARL is useful only under the linear assumption between the cost of out-of control and the delayed time to signal.