# If I know x-bar, spec limits, and Cpk, can I calculate the control limits?

B

#### brgman63

If I know x-bar, spec limits, and Cpk, can I calculate the control limits?

#### Chennaiite

##### Never-say-die
Trusted Information Resource
If I know x-bar, spec limits, and Cpk, can I calculate the control limits?
What are your objectives ? Why do you want to do it ?

D

#### Duke Okes

Yes you can, but you'll have to back the std deviation out of the Cpk calculation.

#### Bev D

##### Heretical Statistician
Super Moderator
you also need to know the subgroup size and if it's rational.
but as stated earlier - why would you want to do that?
what good are the control limits if you don't have the subgroup data in time series??
why not just calculate the 'old fashioned' (correct) way from the time series subgrouped data?
doing it in the way you propose is frought with potential error and I dont' see any value in it?

S

#### statdoug

As Bev stated, this approach is frought with hazards. I am assuming that you no longer have the data. Without knowing the way the data was gathered, it is difficult to know what sigma(hat), if that was what the Cpk was calculated from, represents.

The formula is simple, |xbar - closest spec. limit|/(3xCpk) yields the original sigma(hat) value.

Divide this by the square root of the sample size you plan to use, and use Xbar +/- 3 * this value.
(note we divided by 3 in the first formula, then multiply by three in the second. Obviously we could leave "3" out completely, but conceptually it is helpful.)

Because of the unknowns involved, without details of how the data was gathered, and how the original sigma value was calculated, these limits should only be viewed as very preliminary. As soon as you have enough data to see how the process is running under the sampling plan that you are using, you should abandon these limits and get ones that are calculated correctly in order to determine what the process is really doing.

Bear in mind, that, without the original data, you can not be sure whether the range was in control in the original data, whether OOC ranges were eliminated or not, how many subgroups were used, and alot of other potential problems. Proceed at your own risk.

#### Jim Wynne

If I know x-bar, spec limits, and Cpk, can I calculate the control limits?
Welcome to the Cove.
Where did the Cpk number come from?

#### Bev D

##### Heretical Statistician
Super Moderator
good question! (of course)
there are several critical issues with Cpk:
• is it long term or short term formula?
• which standard deviation was used? within subgroup or total?
• What was the sample plan for Cpk? one lot, 30 consecutive parts, 30 random parts from across multipel lots, multiple subgroups, etc.
• was the process stable when Cpk was calculated?

the control limits are based on an estimate of the between subgroup variation from the within subgroup variation...its not quite as straight forward as the formula statdoug provided - it could be right or it could be wrong depending on which standard deviation was used for the Cpk value.

S

#### statdoug

it could be right or it could be wrong depending on which standard deviation was used for the Cpk value.
If the "standard" standard deviation was used wouldn't the term have been Ppk rather than Cpk?

#### Jim Wynne

If the "standard" standard deviation was used wouldn't the term have been Ppk rather than Cpk?
If it was an actual population standard deviation, it would be Ppk, but since there seems to be an element of confusion on the part of the OP, we can't be sure that the distinction has meaning for his index value.

G S30100 steel bar spec - related specs, ASTM or AMS? ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 2
Group checkout with bar code Using GAGEpack Software 1
Need journal and reference of abnormal bar chart SPC Statistical Analysis Tools, Techniques and SPC 4
Minitab 19 Anova or X bar # of distinct catagories Using Minitab Software 2
1 How to measure straightness on a HEX Long Bar Manufacturing and Related Processes 7
Can subgroup size change daily? (X-bar & R) Capability, Accuracy and Stability - Processes, Machines, etc. 5
The ARL for an X bar Control Chart (n = 5) Statistical Analysis Tools, Techniques and SPC 5
G I-Chart and X bar Chart Control limits Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 3
CE Marking of Robotic Devices which use 5 Bar Pneumatics CE Marking (Conformité Européene) / CB Scheme 3
L How to interpret the average R bar Value shown in the R Chart Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 2
How to evaluate hazards in using bar code scanners in chemical manufacturing Occupational Health & Safety Management Standards 1
A Bar Lights vs LED-606 in vision inspection Inspection, Prints (Drawings), Testing, Sampling and Related Topics 1
J SST .625 dia Cold Rolled 303 bar and Magnetism Manufacturing and Related Processes 6
J Determining if there is Tin Plating on an Aluminum Bar Inspection, Prints (Drawings), Testing, Sampling and Related Topics 6
O Main difference between X-bar sigma chart / X-bar range chart Statistical Analysis Tools, Techniques and SPC 4
M Interpreting X bar and R Control Charts Statistical Analysis Tools, Techniques and SPC 2
M What is the difference between X Bar - R Charts and Average Chart? Statistical Analysis Tools, Techniques and SPC 7
B New website for AIAO-BAR - Unaccredited Accreditation Body ASQ, ANAB, UKAS, IAF, IRCA, Exemplar Global and Related Organizations 33
Does the NIST certificate that came with my new ball-bar have any value? General Measurement Device and Calibration Topics 8
D One-Two-Three Sigma Control Limits - Calculating Control Limits for X-bar Charts Statistical Analysis Tools, Techniques and SPC 3
Bar Sealer vs. Impulse Sealer for Medical Pouch Heat Sealing Qualification and Validation (including 21 CFR Part 11) 4
S What decision rules should be applied for x bar-R chart? Statistical Analysis Tools, Techniques and SPC 10
I-MR Chart vs. X-bar & R Chart - Differences Statistical Analysis Tools, Techniques and SPC 8
D ANOVA vs. X bar & R - MSA Study in Mintab - Which to use and why? Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1
R Calculation Mean for Control Chart -X Double Bar Statistical Analysis Tools, Techniques and SPC 13
X Bar R chart - Interpretation in MSA study Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 2
C 1040 vs. 1040 Modified Bar Stock - Material Question Manufacturing and Related Processes 7
M How to Fix the Standard Bar of a Screw Thread Micrometer General Measurement Device and Calibration Topics 9
J ANOVA vs. X-bar/R Calculations Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 5
M X-Bar Chart - CQE Problem to Solve Statistical Analysis Tools, Techniques and SPC 3
K Individual x Chart - Why use the equation is barX+2.66 bar(MR) Statistical Analysis Tools, Techniques and SPC 6
S Validity of Craig Hane's Global Local Index for X-bar R Chart Assessment Capability, Accuracy and Stability - Processes, Machines, etc. 3
Writing the symbol for R bar bar (double bar) in Excel Excel .xls Spreadsheet Templates and Tools 3
D For Reference Only or Calibration/Verification - Tape Measures for cutting bar stock ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 26
S Medical Gas Pressure Regulators - Anybody had testing conducted at 450 bar? ISO 10524 Other ISO and International Standards and European Regulations 5
D Relying on Supplier Records for Material Traceability - Bar stock and forgings ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 11
Subjective vs Objective Finish Issues - Stainless Steel Bar Inspection, Prints (Drawings), Testing, Sampling and Related Topics 20
Q X-bar R chart question from CSSBB - QCI CD Professional Certifications and Degrees 2
M ANOVA / X Bar R Results are different - Why is the difference is so great? Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 9
A Monitoring Out-of-control situations on X-bar and R chart Statistical Analysis Tools, Techniques and SPC 15
M CE Product Registration Bar Codes for each Product - Anyone? EU Medical Device Regulations 2
K Bar coding of gages on usage instead of time General Measurement Device and Calibration Topics 4
Brass bar stored in green wood boxes tarnished Manufacturing and Related Processes 5
Experts on Aluminum? 2024 T4 and T351 Bar Question Manufacturing and Related Processes 9
G Preventive Maintenance for Assembly Line Bar-Code & General Printers - Necessary? IATF 16949 - Automotive Quality Systems Standard 4
D Writing the symbol for X bar in Excel? Excel .xls Spreadsheet Templates and Tools 11
Portable Hardness Testing and Testers for Incoming Bar Stock Testing Inspection, Prints (Drawings), Testing, Sampling and Related Topics 8
C Gage R&R for Uni-Micrometers on a rod or bar OD (Outside Diameter) Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 7
J ANSI Bar Code Validator MSA (Measurement Systems Analysis) Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 3
J Large CMM Calibration - Tetronom or Giant Ball Bar General Measurement Device and Calibration Topics 6