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 worthy instrument for detecting and diagnosing chronic shifts in sequence of readings. it really is utilized in conventional statistical strategy keep watch over (SPC) settings resembling production, yet can also be potent in settings as assorted as team of workers administration, econometrics, and standard info research. it's a necessary instrument for the standard specialist. This booklet covers CUSUMs from an application-oriented point of view, whereas additionally offering the basic theoretical underpinning. it's obtainable to somebody with a uncomplicated statistical education, and is aimed toward caliber practitioners, lecturers and scholars of caliber methodologies, and folks attracted to research of time-ordered information. 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 facts, collage of Minnesota. he's a Fellow of the yankee Statistical organization, a Member of the foreign Statistical Institute and a Senior member of the yankee Society for qc. His paintings on multivariate CUSUMs gained 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 yank 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 yank Statistical organization, the yankee Society for quality controls, and the army Operations study Society, the place his paintings on functions of CUSUMs to dealing with sexual harassment was once nominated for the 1998 Barchi prize. he's Editor of Mathematica

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8 standard deviations. 8 for the segment leading out of the point {m, 8 m }. A reasonable way to do this is to draw a line of slope midway between these two levels, that is of slope 004. If the CUSUM remains close to or below this line, you will conclude that the mean has not shifted. 8 is more believable than is slope zero. We make this concrete by saying that if any future point is more than some threshold height h above this line, that will constitute the evidence of the shift. 4 located h units vertically above the point {m,8m }.

I=m+l In the second of these two summations, the summand is distributed as N(o, a 2 ). L) tv N[(n - m)o, (n - m)a 2 ]. 3) i=m+1 In other words, the average value of the CUSUM at time n > m is (n - m)o. This means that starting from the point (m, Cm), the CUSUM on average will trace out a path centered on a line of slope o. 5 illustrates a CUSUM of a process that has gone out of control at m = 50. The in-control distribution was N(O,l). 5. Notice the change to linear drift from no drift. This is the basis for using the CUSUM to diagnose shifts in mean.

This determines the reference value k. We then select the desired in-control ARL to meet our particular needs. Once the ARL and k are determined, the value of the decision interval h, follows, and may be found from tables or software. In the next chapter, we continue our examination of CUSUMs of normal data. 5 Further reading We have concentrated on designing by choosing the in-control and out-ofcontrol means. Bissell's (1969) discussion paper had a perspective largely lost from more recent writings, connecting the CUSUM design with acceptance sampling ideas of acceptable and rejectable quality levels.

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