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M.S.Ramaiah School of Advanced Studies CuSum Chart AMT 2506 Shanmuga Raja .B (BVB0912004) Module leader : Mr. Sandeep .N 1

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Basic construction and interpretation of CUSUM chart is explained

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M.S.Ramaiah School of Advanced Studies

CuSum Chart

AMT 2506

Shanmuga Raja .B(BVB0912004)

Module leader : Mr. Sandeep .N

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M.S.Ramaiah School of Advanced Studies

Introduction

Cumulative sum, simply known as CUSUM chart is a sequential analysis technique. Implies the calculation of cumulative sum of deviation of each sample through which,

•Change detection is monitored with high sensitivity.

•Efficient in detecting small shifts in the mean of process.

•Stopping rule in case of out of control process.

•Use all historic information unlike Shewart chart.

•Can be used for variables as well as attribute data

•Immediate action can be announced based on trend pattern.

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M.S.Ramaiah School of Advanced Studies

Why CuSum?

CuSum charts are applied because of two main reasons,

Sensitivity in small changes in mean.X-bar and Range or X-bar and S control chart with large subgroup increase sensitivity. But, Individual data chart doesn’t offer required sensitivity compared to CuSum.

Risk mitigation.Shewart charts depicts out of control process in +/-3 sigma levels with sufficient data. CuSum can propose control within 1-1.5 sigma with less data.

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M.S.Ramaiah School of Advanced Studies

Application

CuSum charts are used as a management technique rather than shop floor chart because the change significance is shown through slopes and their interpretation require care.

Used as a tool for,

•Forecasting (actual v/s forecasted sales)

•Employee engagement (recruitment, absenteeism)

•Production levels (detection of process changes)

•Plant breakdowns (maintenance performance)

Widely used in continuous process like chemical processing, medical services to check the implementation level and bring them into control immediately.

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M.S.Ramaiah School of Advanced Studies

Differences

Individual chart showing the process within control based on runs.

Change in process control detected with same data using CUSUM.

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M.S.Ramaiah School of Advanced Studies

CuSum construction

Week Sample Week Sample Week Sample Week Sample Week Sample Week Sample

1 24 11 24 21 27 31 21 41 27 51 20

2 27 12 27 22 22 32 19 42 20 52 19

3 22 13 24 23 24 33 20 43 21    

4 35 14 23 24 27 34 28 44 25    

5 27 15 25 25 28 35 20 45 19    

6 23 16 27 26 23 36 23 46 22    

7 27 17 29 27 26 37 25 47 24    

8 28 18 28 28 31 38 21 48 19    

9 25 19 24 29 29 39 18 49 25    

10 20 20 29 30 25 40 21 50 28    

Lets have an example showing the downtime hours for 52 weeks tabulated as below

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M.S.Ramaiah School of Advanced Studies

CuSum construction

• Calculate the average downtime

• Select the target value, TTwo things can be considered, which are selecting the mean as target or value near to mean whichever is appropriate. (T= 24.2)

• Calculate the difference between individual and target x-T

x 24 27 22 35 27 23x - T -0.2 2.8 -2.2 10.8 2.8 -1.2

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M.S.Ramaiah School of Advanced Studies

CuSum construction

• Calculate the CUSUM score (cumulative value from previous data),

• Find the maximum and minimum CUSUM score to define the limits of scale.

x 24 27 22 35 27 23x - T -0.2 2.8 -2.2 10.8 2.8 -1.2

∑x - T -0.2 2.5 0.3 11 13.8 12.6

Min -0.2 Max 52.2

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M.S.Ramaiah School of Advanced Studies

CuSum construction

• Determine scaling, unless a suitable convention is used the interpretation becomes difficult as shown below,

• The thumb rule used is to measure one observation in horizontal into 2 times the standard deviation in vertical axis.

S= R / D2* = 3.18 / 1.129 = 3.382s= 6.76 rounding off to 5

2s

1x* Constant based on sample size.

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M.S.Ramaiah School of Advanced Studies

CuSum construction

• Plot the CUSUM chart.

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M.S.Ramaiah School of Advanced Studies

CuSum Interpretation

• Interpretation intent is on the slope and changes in the slope.

• The changes in slope can be considered as,

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M.S.Ramaiah School of Advanced Studies

CuSum Interpretation

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M.S.Ramaiah School of Advanced Studies

CuSum Control limits

The control limits are different from what is used in Shewart charts. Control specification can be defined by,

•V-Mask.•Decision interval.

V-Mask:Most popular method in CUSUM to find, out of control plots.

Week 29

In-control Out-of-control13

M.S.Ramaiah School of Advanced Studies

CuSum Control limits

• Draw horizontal datum line.

• Draw CB and DC with 5 standard deviation apart.

10 SamplesF

• Take a 10 observation distance from C to F.• Draw vertical line AF with 10 standard deviation.• Connect the line AB• Repeat on other side

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CuSum Control limitsDecision Interval:

•Line AB is drawn from target to week 29.•Draw AC with 5 standard deviation.•At 10 observation from A draw line DE with 10 Standard error.•Join CE until it cuts the curve. If happens there is a change.

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CuSum Limitations• CUSUM is relatively slower to respond in larger shifts.

• Special patterns are hard to interpret and analyze.

• Setting up a CUSUM chart is bit time consuming and laborious.

• The construction scheme changes for handling variable and attribute data.

• For accurate results the CUSUM design should be carefully considered.

M.S.Ramaiah School of Advanced Studies

References

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Steven Wachs (2010) “What is a CUSUM Chart and When Should I Use One?”, [online] available from <http://www.integral- concepts.com/docs/What%20is%20a

%20CUSUM%20Chart%20and%20When%2 0Should%20I%20Use%20One.pdf> [09 July 2013]

Unknown (2004) “Quality control methods”, [online] available from <http://sites.stat.psu.edu/~dhunter/401/materials/PPCh16mod.ppt> [10 July 2013]

Unknown (2005) “An introduction to cusum (cumulative sum) charts”, [online] available from

<http://v5.books.elsevier.com/bookscat/samples/9780750665292/9780750665292.PDF> [10 July 2013]

John S. Oakland (2003) “Statistical process control”, 5th edn, Burlington MA: Butterworth-Hienemann.

Wikipedia (2003) “Cusum”, [online] available from <http://en.wikipedia.org/wiki/CUSUM> [10 July 2013]

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