Quality Progress - January 2015 - 63

ONE GOOD IDEA BY VLADIMIR SHPER Concerning the CUSUM A simple way to analyze a cumulative sum chart using Excel IT IS WELL KNOWN that the cumula- Example with Excel these lines are shown in columns H and I of tive sum (CUSUM) technique is one of the Figure 1 shows a CUSUM chart construct- Online Figure 1). To draw a V-mask, it is necessary to most widely used tools in data analysis. ed from data in Donald J. Wheeler's Ad- The technique is usually recommended vanced Topics in Statistical Process Con- copy the set of cells that corresponds to for monitoring the changes in process trol.5 All the values of this curve are taken your lines (in this example, cells F11:G15) characteristics because CUSUM charts from column E (Online Figure 1, which and place it into a cell of interest. Doing "are much more effective than Shewhart can be found on this column's webpage at this, you should take into account the charts in detecting small and moderate- www.qualityprogress.com). This is a typi- length of the V-mask arm or how many sized sustained shifts in the parameters cal graph calculated from the formula Si = cells you used for depicting the sloping of the probability distribution of a quality Si-1- T + xi, in which T denotes a target of lines. characteristic." the process. In this example, T = 50. 1,2 3 Contrasted with simple Shewhart If the regions of two successive draw- 6 Calculate the parameters of V-mask as ings overlap, erase the previous one. Otherwise, several extra lines will appear charts in which you visually analyze it's described in any guide. Again, using process stability-seeing whether there data from Advanced Topics in Statistical and make the picture a bit ambiguous. A are points beyond the control limits-vi- Process Control: H = 4,876 and K = 1,84, comparison with data in Advanced Topics sual analysis of a CUSUM chart is rather in which H is a critical distance of V-mask in Statistical Process Control8 shows that tiresome. It requires that you construct a and K is its slope (Online Figure 2). Now, Online Figure 3 leads to the same results so-called V-mask with arms pointing to the choose any cell in the column next to col- as a traditional V-mask. left and a central point, which should be umn E (for example, E15 in Online Figure placed on each point of the process as it 1) and construct two straight lines with change the parameters of V-mask. Such is plotted. the slope K starting at points deviated a simple technique may be useful for from the chosen point by H units. quality practitioners, especially when you Due to such inconvenience, most textbooks recommend an algorithmic (or 7 In cell F15, enter the formula: =E15 - table) method to analyze the process sta- $L$30 ($L$30 contains the value of H). In bility while working with CUSUM charts.4 For cells F14 and G14, enter =E15 - $L$30 to plot a moving V-mask on a CUSUM - $L$29 and =E15 + $L$30 + $L$29, respec- graph by using traditional Excel software. tively ($L$29 contains the value of K). consider the pervasiveness of the Excel cell G15, enter the formula: =E15 + $L$30. But there's a simple procedure for anyone Apparently, Excel allows you to easily For cells F13 Cumulative sum plot / FIGURE 1 20 0 and G13, you have: =E15 - $L$30 - 2 * $L$29, =E15 + $L$30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 -20 -40 + 2 * $L$29, and so on. As a result, you can obtain some- application. QP REFERENCES 1. Donald J. Wheeler, Advanced Topics in Statistical Process Control, SPC Press, 1995. 2. Douglas C. Montgomery, Statistical Quality Control, sixth edition, 2009. 3. William H. Woodall, "Controversies and Contradictions in Statistical Process Control," Journal of Quality Technology, 2000, Vol. 32, No. 4, pp. 341-350. 4. Montgomery, Statistical Quality Control, see reference 2. 5. Wheeler, Advanced Topics in Statistical Process Control, see reference 1, chapter 13, Table 13.1. 6. Wheeler, Advanced Topics in Statistical Process Control, see reference 1. 7. Ibid, p. 293. 8. Ibid, chapter 13, Figures 13.3-13.5. thing like Figure 4. -60 Here, crimson lines -80 show the mask arms -100 -120 Source: Donald J. Wheeler, Advanced Topics in Statistical Process Control, SPC Press, 1995, chapter 13. pointing to the left, and yellow lines for those pointing to the right (the values for VLADIMIR SHPER is an associate professor at the Moscow Institute of Steel and Alloys in Russia. He holds a doctorate in reliability from the All Russian Electrotechnical Institute in Moscow. Shper is a senior member of ASQ. January 2015 * QP 63 http://www.qualityprogress.com

Table of Contents for the Digital Edition of Quality Progress - January 2015

Up Front
LogOn
Expert Answers
Keeping Current
Mr. Pareto Head
Total Quality’s Leader
Narrow(er) Focus
Dissecting the Differences
Separate Steps
Innovation Imperative
Measure for Measure
Quality in the First Person
Career Corner
Statistics Roundtable
Standards Outlook
QP Toolbox
QP Reviews
One Good Idea
Back to Basics

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