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

By Douglas M. Hawkins, David H. Olwell

Cumulative sum (CUSUM) keep watch over charting is a beneficial instrument for detecting and diagnosing chronic shifts in sequence of readings. it truly is utilized in conventional statistical method keep watch over (SPC) settings akin to production, yet can also be powerful in settings as varied as body of workers administration, econometrics, and traditional facts research. it's a vital software for the standard specialist. This e-book covers CUSUMs from an application-oriented perspective, whereas additionally supplying the fundamental theoretical underpinning. it's obtainable to someone with a simple statistical education, and is geared toward caliber practitioners, lecturers and scholars of caliber methodologies, and folks attracted to research of time-ordered information. The textual content is supported through an internet site containing CUSUM software program and information units. Douglas M. Hawkins is Chair of the dept of utilized data, college of Minnesota. he's a Fellow of the yankee Statistical organization, a Member of the overseas Statistical Institute and a Senior member of the yank Society for qc. His paintings on multivariate CUSUMs received him the Ellis R. Ott Award for the simplest 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 yankee Society for qc, and the army Operations examine Society, the place his paintings on purposes of CUSUMs to handling sexual harassment used to be nominated for the 1998 Barchi prize. he's Editor of Mathematica

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If the mean undergoes a step change, then the CUSUM de- velops a linear drift, and its distribution will center instead on a line whose slope 8 equals the shift in mean. The diagnosis of the CUSUM therefore consists of distinguishing the no-drift in-control behavior from the lineardrift behavior following a mean shift. In principle, the mean could change in more complex ways and the CUSUM could diagnose these more complex shifts. Suppose that instead of a step change the mean develops a slow linear drift ; specifically, suppose the mean of Xn for n > m was IL+(n-m)8.

In "variable sampling intervals" (VSI) methods, this is not the case, and sampling frequency is increased when there are early indications of a possible out-of-control, and decreased when these indications go away. Reynolds et al. (1990) showed how the use of VSI with CUSUMs can improve their performance. A variant that combines the CUSUM with a short-term SPRT is given in Assaf and Ritov (1989). 3 More about normal data All models are wrong, but some are useful. G. E. P. Box The most common application of CUSUMs is controlling the mean of a stream of process data modeled by the normal distribution.

CUSUM charts allow the prompt detection of out-of--control states, and provide estimates of when the change occurred, and of the magnitude of the change. We illustrated with charts for detecting mean shifts for a normal process. We derive CUSUM schemes for the key members of the exponential families in subsequent chapters. In the next chapter, we discuss the design of a CUSUM chart. This design involves selecting k and h so that the resulting chart has "good" properties. 11 Further reading Walter Shewhart developed the original "Shewhart" scheme, and his book Economic Control of Quality of Manufactured Product is the classic work on Shewhart Charts.

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