# Control Chart Rules - Trend and Statistics Explainations

Y

#### YKT

This may sound sily to some, but probably some of the statistic gurus might be able to help me out in explaining the control chart rules....

What is the statistic explaination for the following ?

1. Why must be 7 consecutive points that continue to increase is consider a trend ? Why not less than it ?

2. Same goes for runs...why 7 points on one side is consider a run ? or 10 out of 11 points on one side of the center line consider a run ?

Anyone care to explain on the statistical explaination ?

Many thanks

M

#### M Greenaway

All to do with probability.

A process running in control should be randomly distibuted around the mean value. It is highly improbable that a run that shows seven points above or below the mean is a random distribution around that mean.

So in a nutshell - probability.

D

#### D.Scott

Hi YKT - welcome

Think of flipping a coin. it has a chance of landing either heads or tails. For every flip the posibility is 1 in 2 (1/2) that it will land heads. If you flip it once and it is heads, the chance of it happening on the next flip is still 1 in 2 (1/2).
Here's the catch - what is the chance it will be heads 2 times in a row? to find out you multiply the chance of the first time by the chance of the second time or 1/2 X 1/2 = 1/4. Therefore you can see the chance of 2 in a row is 1 out of 4 times. For 3 times in a row you do the same thing 1/2 X 1/2 X 1/2 = 1/8. So 3 in a row is likely to happen only 1 in 8 attempts. The higher the number of recurrances, the less likely it becomes statistically.
Now think of your control chart - above the center line is "heads" and below the center line is "tails". To get 7 in a row above the line would be 1/2 X 1/2 X 1/2 X 1/2 X 1/2 X 1/2 X 1/2 = 1/128. You can see it is highly unlikely for this to happen UNLESS SOMETHING HAS CHANGED. When you see the condition it should signal to you that "Something doesn't look right" and you can investigate the process to find what has changed.
The same principle applies to trends of up and down. Think of up as heads and down as tails. Trends can be indicated with fewer than 7 points and depending on how robust your process were and how dependable the data you may look for indicators as low as 5 in a row.

Hope this helps a little

Dave

A

#### Atul Khandekar

. Trends can be indicated with fewer than 7 points and depending on how robust your process were and how dependable the data you may look for indicators as low as 5 in a row.
I have read somewhere (I'll have to dig up that reference-don't have it at hand right now) that the rule of 7 points ascending/descending should be discontinued as it tends to increase the rate of false alarm.

D

#### Darius

Atul you posted the article in Precontrol ( 22nd December 2002)

http://www.asq.org/pub/jqt/past/vol32_issue4/qtec-341.pdf

I am agree that 7 points going up or down are almost imposible to happen, because of the natural noise of the variable, the measurement error, etc, the case that is likely to happen is in a continuos process (like taking samples in a chemical batch, where a chemical reaction is happening), but in this case is what is expected to happen (no special events), so I am agree with you, 7 points should be discontinued as it tends to increase the rate of false alarm.

Darius

:thedeal:

K

What are the calculations ( formulas, constants ) for a single sample size of X bar & R? Help anyone?

R

#### roland_lu

Darius said:
Atul you posted the article in Precontrol ( 22nd December 2002)

http://www.asq.org/pub/jqt/past/vol32_issue4/qtec-341.pdf

I am agree that 7 points going up or down are almost imposible to happen, because of the natural noise of the variable, the measurement error, etc, the case that is likely to happen is in a continuos process (like taking samples in a chemical batch, where a chemical reaction is happening), but in this case is what is expected to happen (no special events), so I am agree with you, 7 points should be discontinued as it tends to increase the rate of false alarm.

Darius

:thedeal:

AIAG SPC 2nd Edition indicates 6 in a row, all increasing or all decreasing, shall be identified as out-of-control condition, which makes you wonder the more alarms, the better for the big 3.

#### Jim Wynne

What are the calculations ( formulas, constants ) for a single sample size of X bar & R? Help anyone?
Xbar/R charting is intended for use with rational subgroups, not individuals. The "R" part of it deals with subgroup ranges, and if there are no subgroups, there are no ranges. You need to chart individuals (X and moving range, for example, or use some other sort of analysis. In this thread I referred you to the online NIST engineering statistics handbook; you might want to refer to it for information on Individuals Control Charts.

X-MR Control Chart Rules (Particularly the MR) Statistical Analysis Tools, Techniques and SPC 3
Informational Control Chart Interpretation - General "Rules" Statistical Analysis Tools, Techniques and SPC 92
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
Control chart selection of multiple batches review Statistical Analysis Tools, Techniques and SPC 6
Linking control chart with control plan Statistical Analysis Tools, Techniques and SPC 5
Quality Control (stability) Chart for CMM's - How the control limits are to be calculated Capability, Accuracy and Stability - Processes, Machines, etc. 2
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
What is "setup control chart"? Statistical Analysis Tools, Techniques and SPC 2
Redesigning our process flow chart, PFMEA and Control Plan Process Maps, Process Mapping and Turtle Diagrams 4
D Control chart applicable? Percentage of compliance with a standard Statistical Analysis Tools, Techniques and SPC 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
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
How to define Root Cause when some points are out of control chart Statistical Analysis Tools, Techniques and SPC 6
The ARL for an X bar Control Chart (n = 5) Statistical Analysis Tools, Techniques and SPC 5
P-Chart Control Limit Calculation help Statistical Analysis Tools, Techniques and SPC 1
A Complete Control Chart Decision Tree Statistical Analysis Tools, Techniques and SPC 5
Variation Study on Mined Material - What do you call it (not a control chart) Statistical Analysis Tools, Techniques and SPC 7
G I-Chart and X bar Chart Control limits Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 3
S Regression Control Chart - Process Capability Statistical Analysis Tools, Techniques and SPC 18
J Control Chart Pattern Detection Statistical Analysis Tools, Techniques and SPC 3
R Control Chart Constants and Confidence Interval Statistical Analysis Tools, Techniques and SPC 7
P Specification and Tolerance in Stability Control Chart Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 9
What is an "X-Rs" Control Chart? Statistical Analysis Tools, Techniques and SPC 4
I What is an Ideal Control Chart for Hospital Surgery Infections? FMEA and Control Plans 2
M Shewhart Control Chart for SPC In Excel - Explain the yellow and red marked column Statistical Analysis Tools, Techniques and SPC 2
K Advice on Calculating Control Chart Control Limits Statistical Analysis Tools, Techniques and SPC 13
J Statistical Significance and SPC Control Chart Reports Statistical Analysis Tools, Techniques and SPC 9
P SPC Data Collection and Control Chart Type question Statistical Analysis Tools, Techniques and SPC 4
R XBar & R Chart Spreadsheet to apply a Control Process Statistical Analysis Tools, Techniques and SPC 1
Control Chart for Non-Manufacturing Process Indicators - Is it worth? Statistical Analysis Tools, Techniques and SPC 1
O Is it an Assignable Cause only if the Control Chart says so? Statistical Analysis Tools, Techniques and SPC 16
C Control Chart Roadmap Template Document Control Systems, Procedures, Forms and Templates 0
Shewhart Control Chart - ISO/TS 13530:2009(E), Page 22. General Measurement Device and Calibration Topics 3
MSA (Measurement System Analysis) - Do we have control of all states in the chart? Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 5
H Control Chart applications in Cement Industries Statistical Analysis Tools, Techniques and SPC 2
T Implementing SPC - Control Chart for Individual Measurements Statistical Analysis Tools, Techniques and SPC 9
"Control" as used in 4.1 c) - Process Flow Charts (Process Sequence Chart) ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 12
I Control Chart for Mortality Rate on Broiler Farms Statistical Analysis Tools, Techniques and SPC 4
G Control Chart Selection for Crimping Operations for RJ 45 Plugs Statistical Analysis Tools, Techniques and SPC 5
K When to create a new Control Chart? Quick question Statistical Analysis Tools, Techniques and SPC 4
T Control Chart - Salt Spray Test Hours - Powder Coated Parts Statistical Analysis Tools, Techniques and SPC 3
S Calculation of Upper and Lower Control Limits for Control Chart? Statistical Analysis Tools, Techniques and SPC 7