CUSUM Chart - Can some one throw some light on use and how to interpret?

C

cyberspider

#1
#1
Can some one throw some light on use of CumSum Chart and how to interpret the result. Only thing I know is, there are some better features compared to Shewart for detecting smaller shifts, but how ?- this 'how' is not clear.

When ever I tried to plot a CumSum chart in Mintab, I get one 'Red coloured slanting line' and a 'Black coloured' horizontal line on the chart. :bonk: :frust:

Thanks in advance. :thanks:
 
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Q

Qaware

#5
#5
Why CUSUM detects small shifts better.

Can some one throw some light on use of CumSum Chart and how to interpret the result. Only thing I know is, there are some better features compared to Shewart for detecting smaller shifts, but how ?- this 'how' is not clear.
Click to expand...
Hi, maybe I can help you understand the why.
First of all I believe that Minitab uses the tabular method and not the V-mask. The two lines are probably the upper and lower cusum Ci+ and Ci- one for shift in positive direction and one for negative shift of the mean.

Now to why a CUSUM or EWMA is better than Shewhart in detecting small shifts. Its simply because they take historical data into account. On the other hand, for the same reason a CUSUM is not as good as Shewhart at detecting large shifts quickly.
Lets assume a positve one sigma shift in the mean of a process with sigma=1.
To detect this change with a Shewhart chart for individual observations would require approximately 44 datapoints. The beauty of CUSUM is that it accumulates historical data above a chosen level k, usually 1/2 the change you are interested in. The latest value is added to the stored sum of previous observations. The control limits are chosen as a multiple, H of sigma, usually between 4 and 5. Now if k=sigma/2 and H=5 it would take on average 10.4 samples before the sum Ci+ has reached UCL=5*sigma.

Hope this helps you!
 
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Steve Prevette

Steve Prevette

Deming Disciple
Leader
Super Moderator
#6
#6
Acheson Duncan in Quality Control and Industrial Statistics does give the advantages of CUSUM as being better at picking up a small change faster, and also it is easier to locate the time of the change more sharply. There are also less false alarms. In chapter 22 of his book, he does compare and contrast CUSUM versus Shewhart control charts.

In a detailed analysis, he does point out that large shifts will actually be detected faster on the Shewhart charts. Overall, it appears that statistically the CUSUM charts are superior to Shewhart.

For me personally, I have not tried to get folks to use CUSUM. It has been hard enough to get folks to using the Shewhart charts. I believe the ease of understanding and visual portrayal is superior with a Shewhart chart, and the gains in statisical power of CUSUM aren't worth the losses in understandability.
 
Q

Qaware

#7
#7
Good point

Steve Prevette said:
I believe the ease of understanding and visual portrayal is superior with a Shewhart chart, and the gains in statisical power of CUSUM aren't worth the losses in understandability.
Click to expand...
I totally agree with you on this. You should always understand the tools you use in order to be able to draw the right conclusion.
Another way of making it possible to detect small shifts early is the use of an EWMA control chart. This chart is "easier" to understand than a CUSUM. An EWMA chart is also relatively insensitive to data that are not normally distributed, if you choose your weight factor and control limits properly. The EWMA chart can also be used together with a Shewhart chart, the same thing goes for the CUSUM by the way.
However I would suggest that one carefully investigate the benefit of changing from Shewhart to another chart before doing anything. How small shifts in the mean is important to detect? CUSUM and EWMA are a great alternative to an Individuals chart, but if you have an X-bar R chart it might not be such a big difference. Check the OC-curves and compare ARL!!
 
Steve Prevette

Steve Prevette

Deming Disciple
Leader
Super Moderator
#8
#8
You also have to be careful of some of the assumptions made in EWMA control charts. Some assume Poisson (counts) data.
 
C

cyberspider

#9
#9
Thanks all

Thanks to all of you for your expert opinion.

I will stick to Shewart as small shift does'nt mean more to me right now.

Thanks.. :thanks:
 
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