Xbar - R Control Chart taking into account the Probability Limit

J

jp519

How do you construct the Xbar - R control charts taking into account the probability limit (alpha = 0.002)?
All help is appreciated.

Stijloor

Super Moderator
How do you construct the Xbar - R control charts taking into account the probability limit (alpha = 0.002)?
All help is appreciated.
Can someone help this new Member?

Thank you very much.

Stijloor.

reynald

Quite Involved in Discussions
Can someone help this new Member?

Thank you very much.

Stijloor.
Well here is my take on this:

for Xbar R, control limits are given as:
Limits = Xbar +/- A2*Rbar

now A2 is actually equal to 3/[d2*sqrt],
where:
-- d2 is a constant that can be taken from SPC tables,
-- n is your subgroup size
-- 3 is the Z from normal distribution set such that alpha level is very small

There is where alpha level comes in. At alpha = 0.002 or (0.001 at each tail), Z is equal to 3.09025.
Factor that into the equation yields:

Limits = Xbar +/- 3.09025*Rbar/[d2*sqrt]

Note: based on discussion from
Statistical quality control By M. Jeya Chandra 8.3.1.1

Regards,
Reynald

Last edited:

Bev D

Heretical Statistician
Super Moderator
hmmm. mathematically correct, but technically a bad answer as SPC is not intended to be some 'exact' probability test, nor is it based on teh Normal distribution...

Reynald answered the OP's exact question, (I think - unless the OP just wanted to know which menu items to select and where to enter the alpha data in minitab...

However, this really begs the question: WHY would the OP want to chagne the limit from the 'standard' time tested and proven limits??

D

diav615

Like the OP, I would like the answer to this problem.

@ Bev - Is there a way to use Minitab to select the alpha value using the menus?

reynald

Quite Involved in Discussions
However, this really begs the question: WHY would the OP want to chagne the limit from the 'standard' time tested and proven limits??
I totally agree with this, it's just that I encountered this problem in the academe (as a student) that's why im familiar in the approach. As a pratitioner now though I don't use this because I believe that simplicity is one of the selling points of control charting.

Like the OP, I would like the answer to this problem.

@ Bev - Is there a way to use Minitab to select the alpha value using the menus?
As for this, go to usual control charting menus:
STAT>>CONTROL CHARTS>VARIABLES>>Xbar-R
Then go to "XBAR-R OPTIONS" button:
A.) On the estimate tab-->Select Rbar
B.) On the S-Limits tab, you will see
"Display control limits at this multiples of standard deviation"--> input 3.09
C.) On the test tab, select 1 point > K standard deviations from center line
-->set K = 3.09

Then hit on "ok", then "ok"

D

diav615

As for this, go to usual control charting menus:
STAT>>CONTROL CHARTS>VARIABLES>>Xbar-R
Then go to "XBAR-R OPTIONS" button:
A.) On the estimate tab-->Select Rbar
B.) On the S-Limits tab, you will see
"Display control limits at this multiples of standard deviation"--> input 3.09
C.) On the test tab, select 1 point > K standard deviations from center line
-->set K = 3.09

Then hit on "ok", then "ok"
Hi Reynald,

This worked! Many thanks for your help!

Bev D

Heretical Statistician
Super Moderator
Hi Reynald,

This worked! Many thanks for your help!
just because you can doesn't mean you should.

WHY do you want to alter the 'alpha' level? are you a student who is being forced to do this (hopefully only so you see how the math works OR how futile doing it really is). I will repeat: anyone who wants to alter the alpha level doesn't understand SPC and certainly isn't using the approach appropriately. They are only fooling themsleves.

R XBar & R Chart Spreadsheet to apply a Control Process Statistical Analysis Tools, Techniques and SPC 1
Z Xbar/R control chart help (possibly a simple question) Using Minitab Software 1
Variables control chart (XBar & R) template needed Statistical Analysis Tools, Techniques and SPC 2
S Seeking: Control Charts - Xbar R control chart Statistical Analysis Tools, Techniques and SPC 5
D Control limit calculation (Xbar R charts) using Minitab Statistical Analysis Tools, Techniques and SPC 14
The difference between ANOVA and Xbar-R studies Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1
Xbar R chart LCL and UCL in automotive Statistical Analysis Tools, Techniques and SPC 4
IATF16949 audit requirement - Auditor request UCL and LCL must be show Xbar-R, IATF 16949 - Automotive Quality Systems Standard 7
Minitab GRR crossed Xbar and r method macro needed Using Minitab Software 9
K What is the Beta RISK for S chart OF XBAR-S chart Statistical Analysis Tools, Techniques and SPC 0
B How to decide on a sampling size for Xbar-R charts Statistical Analysis Tools, Techniques and SPC 2
S REVERSED Xbar ?R CHART Statistical Analysis Tools, Techniques and SPC 5
I XBar-S A3, B3 and B4 where n>25 Statistical Analysis Tools, Techniques and SPC 4
G GR&R (Gage R&R) Anova versus Xbar Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 4
S My Spread Calcs/Results for Xbar R Charts not Matching Minitab's Statistical Analysis Tools, Techniques and SPC 18
S Should I use Grand Mean or Target Value as the CL for Xbar-R, MA, CUSUM? Statistical Analysis Tools, Techniques and SPC 6
S What should I use for Variable Sample with Size 3, 4, and 5 - xbar-R or xbar-S? Statistical Analysis Tools, Techniques and SPC 4
S Taking samples in a 100 cavity mold for Xbar-R chart Statistical Analysis Tools, Techniques and SPC 1
P Xbar-R Chart - Need help with analysis Statistical Analysis Tools, Techniques and SPC 4
P Xbar-R Chart better than Xbar-S Chart when the subgroup size is small - Why? Capability, Accuracy and Stability - Processes, Machines, etc. 12
When XBar-R wont work... Imported Legacy Blogs 0
K Why is Cpk = lower of (USL-Xbar)/3sig & (Xbar-LSL)/3sig ? Capability, Accuracy and Stability - Processes, Machines, etc. 20
D Variable sample size - Xbar-s charts - How to select A3 and B4 Statistical Analysis Tools, Techniques and SPC 11
D Xbar?R or Xbar-s Statistical Analysis Tools, Techniques and SPC 5
I Calculation of UCL and LCL for SPC charts (Xbar-s) with sub-group sample of 32 pcs. Statistical Analysis Tools, Techniques and SPC 1
D Normality Test Before the Xbar R Diagram is Made? Statistical Analysis Tools, Techniques and SPC 5
S Gage R&R Methods - ANOVA, AIAG, 6sigma Xbar/R, GM - Which to Use Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 3
A Xbar-R chart question - Wire Pull Test - Different Wire Sizes Statistical Analysis Tools, Techniques and SPC 12
A Removing the effect of special causes on Xbar-R chart - Centerless grinding process Statistical Analysis Tools, Techniques and SPC 6
T Gage R&R Excel .xls form and SPC Xbar and R template (lost it.. ) Excel .xls Spreadsheet Templates and Tools 13
L Does anyone use Median Charts instead of Xbar & R charts? Statistical Analysis Tools, Techniques and SPC 3
X Need help / feedback on Xbar/R charts and Cpk/Ppk applicability - Assemblies Capability, Accuracy and Stability - Processes, Machines, etc. 11
Should I use Xbar-R chart? Statistical Analysis Tools, Techniques and SPC 2
C Capability index for one-sided specification? Cpk(max) = (USL-Xbar)/3*s ?? Capability, Accuracy and Stability - Processes, Machines, etc. 13
IATF / AIAG: Control Plans and CC / SC requirements FMEA and Control Plans 1
IATF Process Control Plans not including customer name Manufacturing and Related Processes 13
What should be measurement method in control plan if you are defining Control method as work instruction. Manufacturing and Related Processes 5
Help Needed: Quality Control / Assurance process Quality Manager and Management Related Issues 3
Document Approver System AS9100 Doc Control AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 4
Terms & Conditions Document Control AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 5
Control of Externally Provided Processes, Products, and Services AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 7
Bulk Process (Electroplating), Control Plan, and Process Change IATF 16949 - Automotive Quality Systems Standard 1
ISO 9001:2015 Control of Records - QMS Communications? ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 9
Introducing a document control system benefits Document Control Systems, Procedures, Forms and Templates 5
Effective use of a Risk Register - Bumper sticker or Mission Control ? ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 19
To control the essential design outputs Medical Device and FDA Regulations and Standards News 4
Root cause for outsourced pest control service not in approved supplier list ISO 13485:2016 - Medical Device Quality Management Systems 4
Digital Document Control - Revision ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 13
Process Flow Diagram, DFMEA, PFMEA, Control Plan integrated softwares FMEA and Control Plans 7
Over 60 dimensions CMM measurement in control plan APQP and PPAP 7