Control Chart Constants and Confidence Interval

R

rwhitney

I've read several threads on the calculation of the control chart constants. Concensus is that the constant * variation estimator (e.g. Asub2 * Rbar) estimates sigma * 3 to yield the factor added or subtracted from the central value to net UCL or LCL. Is this estimation quantified by a confidence interval? 90%, 95%, 99%? Maybe buried deep in the calculation or concept?

Steve Prevette

Deming Disciple
Staff member
Super Moderator
No. the control chart limits are "not an exercise in probability" (Dr. Deming).

The control limits are set at 3 standard deviations from the average, a value determined by Dr. Shewhart in 1930 as the best compromise between failure to detect and false alarms across many different data distributions.

Dr. Shewhart invoked the Tchebychev Inequality as theoretical basis to use one number across several distributions, and he tested the results against the Normal distribution, a square distribution and a triangular distribution.

Dr. Wheeler has followed up with several simulation studies, and concluded the level of significance for SPC control limits run from 3% to 5% worst case.

bobdoering

Trusted Information Resource
Dr. Shewhart invoked the Tchebychev Inequality as theoretical basis to use one number across several distributions, and he tested the results against the Normal distribution, a square distribution and a triangular distribution.
Key to note that those distributions need to be from random and independent variation process output. Otherwise, Shewhart's charts do not not work well. Tchebychev Inequality requires random and independent variation to be valid.

Bev D

Heretical Statistician
Staff member
Super Moderator
I'll wade in cautiously here. buried deep in the concept and the calculations of the constants is the core concept that also results in a 'confidence interval'. However, as Steve pointed out, the control chart limits are not confidence intervals. Confidence intervals and control limits can be thought of as cousins. and there is certainly no attempt or ability or need to have a precise probability of any particular result with a control limit as Steve also pointed out.

certainly any particular result has some large or small probability of occurring If the process hasn't changed. The same can be said when comparing two point estimates to each other...but confidence intervals are intended for comparing a very small number of point estimates, typically not differentiated by time but be a different source of change like different vendors, equipment, materials or processes. control limits are used to compare often large numbers of samples that differentiate themselves in time sequence. These different comparisons while similar in some aspects are really very different types of comparisons...

Statistical Steven

Statistician
Staff member
Super Moderator
I've read several threads on the calculation of the control chart constants. Concensus is that the constant * variation estimator (e.g. Asub2 * Rbar) estimates sigma * 3 to yield the factor added or subtracted from the central value to net UCL or LCL. Is this estimation quantified by a confidence interval? 90%, 95%, 99%? Maybe buried deep in the calculation or concept?
I will dip my feet in the water to give you the answer your are expecting. The "probability" is that 3 out of 1000 will be outside the control limits by chance alone. So in the essence the control limit are like 99.73% limits on the distribution of the data.

Statistical Steven

Statistician
Staff member
Super Moderator
The answer of 3 in 1000 is only valid for the Normal Distribution . . .
That is correct, and if you use Xbar charts then the distribution of the means is normal (or approximately normal) regardless of the distribution of the individuals. Of course, if you are a purest, I am probably understating the reality, but I am a realist so 3 out of 1000 is a good estimate.

A Name for the Control Chart Constants (A2, A3, d2, D3 etc) Statistical Analysis Tools, Techniques and SPC 8
E Formulas and Constants - Control Limits for Individual and Moving Range Control Chart Statistical Analysis Tools, Techniques and SPC 2
B Formulas for calculating control chart constants Statistical Analysis Tools, Techniques and SPC 9
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
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
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
Control Chart Metrics/KPI - Measuring Effectiveness of Control Charting System Statistical Analysis Tools, Techniques and SPC 4
L Measurement Uncertainty using Control Chart Measurement Uncertainty (MU) 2
R Calculation Mean for Control Chart -X Double Bar Statistical Analysis Tools, Techniques and SPC 13