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

C

#### cyberspider

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.

Q

#### Qaware

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.
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!

Last edited by a moderator:

#### Steve Prevette

##### Deming Disciple
Super Moderator
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

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.
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

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

C

#### cyberspider

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..

H Steps to Draw a CUSUM Chart with an Example Statistical Analysis Tools, Techniques and SPC 5
Recommendation about h and k values when CUSUM charts are used Statistical Analysis Tools, Techniques and SPC 4
S Should I use Grand Mean or Target Value as the CL for Xbar-R, MA, CUSUM? Statistical Analysis Tools, Techniques and SPC 6
F Cusum Charts - When all the data points are on the target except for 1 Statistical Analysis Tools, Techniques and SPC 1
Z Does Minitab allow standarized cusum (cumulative sum)? Using Minitab Software 2
W Drawing CUSUM Control Charts - Need a simple step by step example Quality Tools, Improvement and Analysis 3
What kind of chart to detect WHEN a in-process NC is about to occur? Reliability Analysis - Predictions, Testing and Standards 2
Organisational chart requirements IATF 16949 - Automotive Quality Systems Standard 5
Xbar R chart LCL and UCL in automotive Statistical Analysis Tools, Techniques and SPC 4
Which chart would be apporiate Quality Tools, Improvement and Analysis 2
Doubt about the correct control chart Statistical Analysis Tools, Techniques and SPC 14
Change color or shape of individual data point in control chart Using Minitab Software 6
Elaborating a control chart with skewed data Manufacturing and Related Processes 4
CQI-15 Welding Health Chart Frequency IATF 16949 - Automotive Quality Systems Standard 1
Microbiological test (USP61, USP62, USP71, ISO 11137.1, ISO11137.2) --- Testing flow chart Other Medical Device Related Standards 0
Control chart selection of multiple batches review Statistical Analysis Tools, Techniques and SPC 4
Linking control chart with control plan Statistical Analysis Tools, Techniques and SPC 5
Organisational Chart-ISO 17025 Laboratory ISO 17025 related Discussions 3
Quality Control (stability) Chart for CMM's - How the control limits are to be calculated Capability, Accuracy and Stability - Processes, Machines, etc. 2
Need journal and reference of abnormal bar chart SPC Statistical Analysis Tools, Techniques and SPC 4
R chart from ANOVA gage R&R test Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 12
Attribute , for example C chart Statistical Analysis Tools, Techniques and SPC 16
SPC procedure / flow chart Statistical Analysis Tools, Techniques and SPC 2
Paynter Chart Example APQP and PPAP 1
Fabric roll inspection - What type of Control Chart to use? Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2
Putting back excluded rows/data points in a control chart Using Minitab Software 0
Control chart and sample time Statistical Analysis Tools, Techniques and SPC 1
Control chart for huge sample size Statistical Analysis Tools, Techniques and SPC 9
Capability analysis - What is going on this chart? Manufacturing and Related Processes 15
How MR (Moving Range) in Z-MR chart is calculated Using Minitab Software 5
What is "setup control chart"? Statistical Analysis Tools, Techniques and SPC 2
Virtual Documentation via Master Flow Chart? Process Maps, Process Mapping and Turtle Diagrams 4
Redesigning our process flow chart, PFMEA and Control Plan Process Maps, Process Mapping and Turtle Diagrams 4
Vigilance process flow chart EU Medical Device Regulations 1
D Control chart applicable? Percentage of compliance with a standard Statistical Analysis Tools, Techniques and SPC 2
I-chart form for GM GP-12 Customer and Company Specific Requirements 2
Link between FMEA, flow chart and control plan FMEA and Control Plans 10
How to do a control chart - Machining product that requires flatness control Capability, Accuracy and Stability - Processes, Machines, etc. 1
China - Where I can get NMPA complete structure/organogram chart and GB/YY format list China Medical Device Regulations 1
K Turtle diagram or process interaction chart - Making it easier for an auditor Process Maps, Process Mapping and Turtle Diagrams 23
Should "Waste" be included as Output in SIPOC Chart? Process Maps, Process Mapping and Turtle Diagrams 8
S Assembly House Process Chart ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 4
Why calculate LCL in P-chart? Statistical Analysis Tools, Techniques and SPC 4
B GM GP-12 Pre-Launch - They asking for a I chart Statistical Analysis Tools, Techniques and SPC 2
SPC Charting frequency calculator for X hi/lo chart Imported Legacy Blogs 0
K Operating characteristic (OC) curve S chart Statistical Analysis Tools, Techniques and SPC 1
K What is the Beta RISK for S chart OF XBAR-S chart Statistical Analysis Tools, Techniques and SPC 0
Understanding control chart and measurement capability Statistical Analysis Tools, Techniques and SPC 2
F Appropriate Control Chart Statistical Analysis Tools, Techniques and SPC 5
S used excel formula calculated the ARL's with Rule1&Rule2 for Shewhart control chart Statistical Analysis Tools, Techniques and SPC 0