Maximum error of a z value from sample data

S

statdoug

#1
The challenge: from a sample of size n, what is the worst-case senario for the proportion below a given spec. limit?

The challenge involves potential that both the estimate of the average and the estimate of the standard deviation are worst-case estimates. This means (for the lower spec. situation) that the average derived from the sample is higher than the true process average, and that the standard deviation derived from the sample is lower than the true process standard deviation. The formulas that I have derived are as follows:

s(max)=sqrt(s^2(n-1)/Chi^2(1-alpha)

z=((xbar-z(alpha/2)(s(max)/sqrt(n))-L.S.))/s(max)

I hope I got all of the parenthesis right.

s(max) is the worst-case estimate of the standard deviation for a given 1-alpha.

((xbar-z(alpha/2)(s(max)/sqrt(n)) is the lowest possible value for xbar based on the maximum possible error of the average >> z(alpha/2)(s(max)/sqrt(n)

the final part is (this value (worst-case xbar), minus the lower spec.) divided by the worst-case estimate of the standard deviation.

Does this formula make sense?
 
Elsmar Forum Sponsor
S

statdoug

#2
C'mon, someone out there must have run in to something like this before. I can't find any similar formula but there must be one out there for figuring the maximum possible defect level based on a sample.
 

Statistical Steven

Statistician
Staff member
Super Moderator
#4
Let's break the problem down. First you want to create a confidence interval on the variance. The using the maximum variability, set a lower (or upper) confidence interval on the mean.

You should use the t-value instead of z to account for the sample size. If you do that, then the confidence interval would be wider. But the confidence interval on the mean using the t-value accounts for the imprecision in the estimate of the mean and standard deviation.

The last piece is the alpha level. The overall confidence interval is wider if you do not partition the alpha to maintain an overall alpha level. This is complex to calculate.

In general your approach is sound, but I have a better solution for you. Use the confidence interval on Cpk and back calculate the value. PM me if you need assistance.
 
Thread starter Similar threads Forum Replies Date
R Clinical accuracy and repeatability of IR(infrared) thermometer, no maximum error criteria is recommended in ISO Other Medical Device Related Standards 11
Marc Definition MPEE - Maximum Permissible Error for Length Measurement Definitions, Acronyms, Abbreviations and Interpretations Listed Alphabetically 0
K Step by Step Gauge R&R with 10% maximum allowable Gauge Error Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1
N ASME B89.1.13 question regarding Resolution and Maximum Permissible Error General Measurement Device and Calibration Topics 3
M Maximum Permissible Error for Monitoring and Measurement Devices General Measurement Device and Calibration Topics 19
N Maximum mains voltage used when applying 60601 IEC 60601 - Medical Electrical Equipment Safety Standards Series 2
D Determining the the maximum number of reprocessing cycles of attachments CE Marking (Conformité Européene) / CB Scheme 2
Marco Bernardi MMC & LMC modifiers and CMM measuring techniques like diameter least squares and circularity or minimum/ maximum diameter Calibration and Metrology Software and Hardware 5
G Need to change KPI we called NC parts (maximum 3%.) to FTQ (first time quality) IATF 16949 - Automotive Quality Systems Standard 4
Judy Abbott Increase the maximum allowable dose for E-beam sterilization Reliability Analysis - Predictions, Testing and Standards 2
M Maximum Height for the stored material or stock materials Occupational Health & Safety Management Standards 1
S How to calculate the maximum allowable hysteresis of a pressure gauge General Measurement Device and Calibration Topics 1
F Irradiation Sterilization Validation Maximum Dose - VDmax 25 method (ISO 11137) EU Medical Device Regulations 2
V Acceptable maximum RSD (relative standard deviation) for an sample size Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1
A Maximum bubble volume for subcutaneous injection IEC 60601 - Medical Electrical Equipment Safety Standards Series 0
D Calibration of a Width Gage Slot with an Attribute Gage - Maximum Width Condition General Measurement Device and Calibration Topics 16
B Maximum Material Condition with Bonus - Determine Cpk for this one kpc Measurement Uncertainty (MU) 2
V Correlating Maximum 'Range' of Values for a given "RSD" (Control Limits) Statistical Analysis Tools, Techniques and SPC 3
M What is the maximum permissible period of delaying the validation of equipment? Other Medical Device Regulations World-Wide 4
C Q as the Datum Maximum Material Condition then MINUS 0.020 Inspection, Prints (Drawings), Testing, Sampling and Related Topics 1
I Minimum and Maximum Validation Batch Size Requirements Qualification and Validation (including 21 CFR Part 11) 3
R Maximum Reverse Speed Limit for Powered Wheelchairs Other US Medical Device Regulations 2
C Maximum acceptable Tolerance - Uncertainty Ratio (TUR) General Measurement Device and Calibration Topics 2
R ISO 14644-1 maximum particulate concentration limits concern Other ISO and International Standards and European Regulations 2
K Maximum Material Condition on Diameter Tolerance Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
L Maximum voltage for IEC 60601? IEC 60601 - Medical Electrical Equipment Safety Standards Series 9
M Zero Tolerancing on True Position using MMC (Maximum Material Condition) Inspection, Prints (Drawings), Testing, Sampling and Related Topics 6
S Aseptic Processing - Maximum SAL using Aseptic Processing for Sterilization Other ISO and International Standards and European Regulations 4
J IEC60825 - Laser Safety - Calculating Maximum Permissible Exposure Correctly Other ISO and International Standards and European Regulations 1
optomist1 Maximum Shift Tolerance Restrained Part - Calculation of Datum Shifts Inspection, Prints (Drawings), Testing, Sampling and Related Topics 7
K Is there a "maximum time limit" for nonconformity to fix? Internal Auditing 11
S What's the maximum post limit in a day? Elsmar Cove Forum ToS and Forum Policies 6
R Maximum allowed eccentricity for any shaft or hole diameter Misc. Quality Assurance and Business Systems Related Topics 7
R Can maximum ambient operating temperature be specified higher than 40C? IEC 60601 - Medical Electrical Equipment Safety Standards Series 5
D Process Capability Study which involves MMC (Maximum Material Condition) Capability, Accuracy and Stability - Processes, Machines, etc. 8
G ANSI & ASME regardless of Maximum Material Condition when none is specified Various Other Specifications, Standards, and related Requirements 3
D ANSI IPC A-610 Maximum Jumper Wires Allowed on Boards by the IPC Standard Various Other Specifications, Standards, and related Requirements 1
D How to inspect maximum allowable contaminate Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2
2 ISO 9001 should be implemented before CMMI for maximum effectiveness? Quality Manager and Management Related Issues 2
M Ergonomics - Human Hand - Maximum force - Wheel/Flywheel - Help ASAP :) Human Factors and Ergonomics in Engineering 8
F How to statistically determine the maximum performance life of a chemical Statistical Analysis Tools, Techniques and SPC 4
Chennaiite Process Capability for a specification with Maximum Material Condition (MMC) Statistical Analysis Tools, Techniques and SPC 4
F Maximum walking distance for assembly line worker Human Factors and Ergonomics in Engineering 28
M What is maximum limit for MU (Measurement Uncertainty) or acceptable criteria? Measurement Uncertainty (MU) 5
S GD&T Rule 1: Gage size for form check at MMC (maximum material condition)? Inspection, Prints (Drawings), Testing, Sampling and Related Topics 9
D How to Measure a Diameter - Average or Maximum/Minimum? Inspection, Prints (Drawings), Testing, Sampling and Related Topics 25
N QMS Scope length limited to 10 to 15 words maximum - How is that possible? ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 5
L Internal threads - Maximum / Minor accept/reject diameter inspection Inspection, Prints (Drawings), Testing, Sampling and Related Topics 6
Q Maximum minor thread diameter of UNF internal threads Inspection, Prints (Drawings), Testing, Sampling and Related Topics 7
E Corrective and Preventive Action - State Maximum time for follow-up required? ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 14

Similar threads

Top Bottom