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
the process. In this example, T = 50.
Contrasted with simple Shewhart
If the regions of two successive draw-
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
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
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
and G13, you have:
=E15 - $L$30 - 2 *
$L$29, =E15 + $L$30
7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
+ 2 * $L$29, and so
on. As a result, you
can obtain some-
1. Donald J. Wheeler, Advanced Topics in Statistical Process
Control, SPC Press, 1995.
2. Douglas C. Montgomery, Statistical Quality Control, sixth
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.
Here, crimson lines
show the mask arms
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
January 2015 * QP 63
Table of Contents for the Digital Edition of Quality Progress - January 2015
Mr. Pareto Head
Total Quality’s Leader
Dissecting the Differences
Measure for Measure
Quality in the First Person
One Good Idea
Back to Basics
Quality Progress - January 2015