期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2002
卷号：32
DOI：10.1155/S0161171202202239
出版社：Hindawi Publishing Corporation
摘要：Cumulative Sum (Cusum) Control Schemes are widely used in
industry for process and measurement control. Most Cusum
applications have been in monitoring shifts in the mean level of a
process rather than process variability. In this paper, we study
the use of Markov chain approach in calculating the
average run length (ARL) of a Cusum scheme when controlling
variability. Control statistics S and S2, where S is the
standard deviation of a normal process are used. The optimal
Cusum schemes to detect small and large increases in the
variability of a normal process are designed. The control
statistic S2 is then used to show that the Cusum scheme is
superior to the exponentially weighted moving average (EWMA) in
terms of its ability to quickly detect any large or small
increases in the variability of a normal process. It is also
shown that Cusum with control statistics sample variance (S2)
and sample standard deviation (S) perform uniformly better
than those with control statistic logS2. Fast initial response (FIR) Cusum properties are also presented.
