Cusum procedure for monitoring variability. (English) Zbl 0954.62570
Summary: In this paper, a CUSUM procedure is given for monitoring for a decrease in the variance (process improvement) as well as a two-sided CUSUM which monitors for both increases and decreases in the variance. The observations are assumed to be independent and normally distributed. The procedure is based on the logarithm of the likelihood ratio of the probability density functions under the two competing hypotheses. Formulae that approximate the average run length of the CUSUM procedure for detecting an increase (or decrease) in the variance of a normal distribution are given. These formulae, when corrected for the overshoot from the boundary, provide a very accurate approximation.
MSC:
| 62P30 | Applications of statistics in engineering and industry; control charts |
Keywords:
average run length; overshoot correction; sequential probability ratio test; Wald’s approximationReferences:
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