# Calculating Lower and Upper 3 Sigma Control Limits

D

#### dmk_miz

I've been stuck on this problem for far too long. I can get numbers close to E, but I am not sure if what I am doing is correct. If somebody has the time to give me a walk through with this I would very much appreciate the help! Thank you!

A manufacturer of fax machines checks samples of fifty units for functionality at the conclusion of the assembly process. The results of ten samples are shown in the table below. Calculate the lower and upper 3-sigma control limits.

Sample # 1-2-3-4-5-6-7-8-9-10

A. (–0.01, 0.09)
B. (–0.01, 0.29)
C. (–0.01, 0.09)
D. (0.00, 0.09)
E. (0.00, 0.29)

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
I've been stuck on this problem for far too long. I can get numbers close to E, but I am not sure if what I am doing is correct. If somebody has the time to give me a walk through with this I would very much appreciate the help! Thank you!

Take your data, divide each by 50. Determine the average of the data (since the sample size is always 50, this makes it easier.

Then use the p-chart calculation for control limits which is the average plus and minus 3 times the square root of (avg x (1-avg) / 50)

#### David-D

##### Involved In Discussions
Good explanation although I'd add that since the calculated lower control limit is negative; you set it equal to zero (since you can't get negative defects).

Since clearly this is an exam type question there is a much faster way to get the right answer by elimination if you understand the underlying concepts. You need to first find the centerline of your control chart (to be able to +/- 3 SD). As you'll find that to be .144 (72 defects /500 samples) you can immediately eliminate choices A, C, and D as all three have both the upper and lower control limits on the same side of the centerline. Then looking at B and E you can immediately also eliminate B since the lower control limit can't be negative. Thus, if you understand the fundental concepts, you can quickly come to the correct answer with very little calculation.

Of course, in actual practice on a production line this shortcut/approach isn't useful for determining actual control limits, but it is very useful as a sanity check to make sure you didnt screw them up. In my experience with the CQE exam, being able to harness 'tricks' to quickly get the answer will allow more time to focus on other questions. Think of it as a time bonus for understanding the concepts above just brute-forcing you're way through the math.

Good luck,

David

K Calculating UCL (Upper Control Limit) and LCL (Lower Control Limit) Statistical Analysis Tools, Techniques and SPC 14
D Calculating Upper-CL/Lower-CL and Process Capability Statistical Analysis Tools, Techniques and SPC 8
D Calculating upper and lower confidence interval bounds Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1
L Geometric Tolerancing and SPC - Calculating position upper and lower control limits Statistical Analysis Tools, Techniques and SPC 36
N Higher Uncertainty Value or Lower Uncertainty Value when Calculating BMC Measurement Uncertainty (MU) 7
C Calculating Process Average Targets for LSL (Lower Specification Limit) Only Statistical Analysis Tools, Techniques and SPC 15
C Calculating Cp and Cpk for Product with only LSL (Lower Specification Limit) Capability, Accuracy and Stability - Processes, Machines, etc. 28
Lean: Conducting Capacity Study, calculating Cycle times on laser cutting machines Lean in Manufacturing and Service Industries 2
Calculating Carbon Footprint in the Organization Miscellaneous Environmental Standards and EMS Related Discussions 2
Calculating your KPIs ISO 13485:2016 - Medical Device Quality Management Systems 7
Calculating Heat Dissipation Manufacturing and Related Processes 1
Calculating Defect Rates ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 4
Formula for Calculating NoGo Major Diameter for UN gages Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
Calculating a weight for a machine for the CE label CE Marking (Conformité Européene) / CB Scheme 0
Remote Support - Calculating Number of Employees IATF 16949 - Automotive Quality Systems Standard 2
Calculating Tolerance of a Panel Meter with a 2 degrees of an Arc General Measurement Device and Calibration Topics 0
Calculating LCL, UCL, Cp, and Cpk in an Excel Spreadsheet Statistical Analysis Tools, Techniques and SPC 3
Product Development - When to start calculating Process Capability Capability, Accuracy and Stability - Processes, Machines, etc. 3
Calculating Reliability for Subsystems in Series Reliability Analysis - Predictions, Testing and Standards 15
Calculating (3rd Party) Audit Days for Company with Seasonal Employees General Auditing Discussions 3
T Formulas for Calculating Coefficients for RTD / PRTD Calibration According to ITS-90 General Measurement Device and Calibration Topics 5
J Calculating part variation from historic data for GRR study Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1
P Purpose of calculating Ta, Tb & R Square in Linearity Study Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1
P Purpose of calculating Uncertainty value in calibration study Measurement Uncertainty (MU) 5
M Calculating MTBF for plug-in PCI cards Reliability Analysis - Predictions, Testing and Standards 2
J Calculating impact force, expressed in lbs, of a 5 lb weight dropped 48 inches Inspection, Prints (Drawings), Testing, Sampling and Related Topics 1
M Calculating Cpk when sample size equals to 1 Capability, Accuracy and Stability - Processes, Machines, etc. 12
D Calculating Cpk on Non-Normal Data Distribution Capability, Accuracy and Stability - Processes, Machines, etc. 10
K Calculating Capability of a process when data is skewed in the upper range Capability, Accuracy and Stability - Processes, Machines, etc. 4
A Calculating Accuracy for a Multimeter General Measurement Device and Calibration Topics 1
M Calculating Coefficients for an RTD (Resistance Temperature Detector) Probe General Measurement Device and Calibration Topics 3
T Calculating Plating/Coating Weight for IMDS RoHS, REACH, ELV, IMDS and Restricted Substances 3
M Calculating Adequate Receiving Inspection Sample Size Statistical Analysis Tools, Techniques and SPC 2
M Calculating Capability of Delivery Performance Capability, Accuracy and Stability - Processes, Machines, etc. 5
K Advice on Calculating Control Chart Control Limits Statistical Analysis Tools, Techniques and SPC 13
B Calculating Combined DPMO and Sigma Level for Two or More Different Work Areas Six Sigma 3
G Calculating the Fraction Defective Confidence Interval for a Lot Statistical Analysis Tools, Techniques and SPC 2
A Calculating Combined Measurement Uncertainty - VDA 5 Measurement Uncertainty (MU) 1
B Calculating Precision to Tolerance Ratio Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 9
D DPPM - Calculating the Defect Rate of a Software Test Statistical Analysis Tools, Techniques and SPC 9
L FMEA - Calculating RPN = S*O*D FMEA and Control Plans 3
I Shewhart Constants vs Central Limit Theorem in calculating Control Limits Statistical Analysis Tools, Techniques and SPC 18
B Please share a template for calculating Cp Cpk Document Control Systems, Procedures, Forms and Templates 3
S Is a Stable Process (within Control Limits) required for Calculating Pp, Ppk? Capability, Accuracy and Stability - Processes, Machines, etc. 6
Calculating the IATF TS 16949 Recertification Audit Man Days - Clarification ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 6
IEC60825 - Laser Safety - Calculating Maximum Permissible Exposure Correctly Other ISO and International Standards and European Regulations 1
P Calculating Process Capability from Data of attached spreadsheet Statistical Analysis Tools, Techniques and SPC 4
I AQL Formula in Excel - Calculating Sample Size based on an AQL Chart AQL - Acceptable Quality Level 8
D Formula for Calculating Warp Measurement of Corrugated Boxes General Measurement Device and Calibration Topics 1
S Need Help Calculating and Implementing Cs - Wright's Index Statistical Analysis Tools, Techniques and SPC 11