Download Cumulative Sum Charts and Charting for Quality Improvement by Douglas M. Hawkins, David H. Olwell PDF

By Douglas M. Hawkins, David H. Olwell

Cumulative sum (CUSUM) keep an eye on charting is a important instrument for detecting and diagnosing continual shifts in sequence of readings. it's utilized in conventional statistical procedure regulate (SPC) settings comparable to production, yet can be powerful in settings as different as group of workers administration, econometrics, and standard info research. it's a necessary software for the standard specialist. This ebook covers CUSUMs from an application-oriented perspective, whereas additionally supplying the fundamental theoretical underpinning. it truly is available to an individual with a simple statistical education, and is geared toward caliber practitioners, academics and scholars of caliber methodologies, and other people drawn to research of time-ordered info. The textual content is supported by means of an internet site containing CUSUM software program and information units. Douglas M. Hawkins is Chair of the dep. of utilized statistics, collage of Minnesota. he's a Fellow of the yank Statistical organization, a Member of the foreign Statistical Institute and a Senior member of the yankee Society for qc. His paintings on multivariate CUSUMs received him the Ellis R. Ott Award for the easiest paper on caliber released in 1993. He has been affiliate Editor of Technometrics and magazine of the yankee Statistical organization. David H. Olwell is affiliate Professor within the division of Mathematical Sciences on the usa army Academy. he's a member of the yankee Statistical organization, the yank Society for qc, and the army Operations examine Society, the place his paintings on functions of CUSUMs to handling sexual harassment was once nominated for the 1998 Barchi prize. he's Editor of Mathematica

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The connection between the Shewhart chart and the superficially very different CUSUM chart is instructive. It helps, first, to illustrate the intuitive idea that the Shewhart chart is very effective for detecting large shifts in mean. In particular, the I chart (a Shewhart chart of individual observations) is the "best" possible chart for detecting shifts in mean of magnitude 6 standard deviations. The connection may also be of some help in selecting the value of m in a Shewhart chart. 50-. 76, a size close to the value 4 or 5 so often used for rational groups in Shewhart charting.

N (n - m)(n2- m "-J + 1)8, (n - m)0"2) . i=m+l The linear drift in the mean of X translates into a quadratic drift for the CUSUM. In practice, it is not easy to distinguish the (locally approximately linear) quadratic drift of this slowly changing mean from the linear drift caused by a step change, so this possibility is of theoretical rather than practical value. Although the CUSUM will respond to the slow drift in mean by signaling, it is not easy to differentiate it from a step change in mean unless you are prepared to wait until quite long after the change.

I=m+l Following the shift in mean from JL to JL + 8, the summand has a normal distribution with mean 8 -k. 10. Decision interval form of the CUSUM. ct which (because C;;; = 0) reduces to k + /(n - m). This is the same estimator that we got by looking at the slope of Cn form of the CUSUM. Similarly, if the downward decision interval CUSUM signals a shift, then the magnitude of the shift can be estimated by 8= -k+C;;/(n-m). ct Note that since is necessarily positive, and C;; is necessarily negative, it is impossible for the estimate of {) to lie between -k and k.

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