Attribute Sampling Calculator
Optimize your quality control with our Attribute Sample Size Calculator. Instantly generate Zero Defect (c=0) plans, assess risk, and visualize performance using our dynamic Operating Characteristic curve.
Updated December 2025
Calculator
LIVE
%
Defect rate to reject.
Inspection Plan
Zero Defect (c=0)
Reject lot if 1+ defects found.
Sample Size
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Operating Characteristic (OC)
Interpreting: If lot has 1% defects, plan accepts it 5.0% of the time.
Assurance 95% Confidence defect rate < 1%
Risk (Beta) 5% Chance of accepting bad lot.
Attribute Sampling Guide
A comprehensive guide to Zero Acceptance Number (c=0) plans. Understand risk, confidence, and why we sample.
The Lottery of Sampling
Sampling is all about probability. Even if defects exist in the lot, there is a chance your sample might "miss" them. This is called Consumer's Risk.
Load a scenario to begin...
What just happened?
If you see red dots in the grid but your sample (circled dots) only picked gray ones, you just accepted a bad lot! This demonstrates why we need statistically calculated sample sizes rather than guessing.
Choosing Confidence Levels
The "Confidence Level" is the mathematical inverse of Risk. If you want 95% Confidence, you are accepting a 5% risk that a bad lot might slip through.
90% CONF
Moderate Control
Used for minor defects or cosmetic issues where a failure isn't critical. You accept a 10% Risk of missing the defect.
Risk: 0.10 95% CONF
Industry Standard
The default for most manufacturing. It provides a strong balance between sample size efficiency and protection.
Risk: 0.05 99% CONF
Critical Safety
Used for medical devices, aerospace, or automotive safety parts. Requires much larger sample sizes.
Risk: 0.01 Confidence Meter Hover list to see levels
Why not 100% Confidence?
To get 100% confidence, you must inspect 100% of the parts. Sampling is, by definition, an exercise in calculating and accepting a specific amount of risk.
AQL vs. RQL: The Battle
The most common confusion in sampling is between "What we expect" and "What we reject".
Expectation
AQL (Acceptable Quality Level)
"The Good Days"
This is the quality level you normally expect from the process. If a lot has this many defects, you want to ACCEPT it most of the time.
Protection
RQL (Rejectable Quality Level)
"The Limit"
Also called LTPD. This is the worst-case scenario. If a lot has this many defects, you want to REJECT it (almost) every time.
The calculator above uses RQL to calculate the sample size for safety.
Operating Characteristic (OC) Curve showing the two zones.
The Formula
For a Zero Acceptance Number (c=0) plan, the math uses the Binomial Distribution approximation. It asks: "How many parts must I check so that the chance of seeing 0 defects is less than my risk threshold?"
The Equation
Sample Size (n)
n=
ln(Risk) ln(1 - p)
Where ln is the natural logarithm, Risk is (1 - Confidence), and p is the RQL defect rate as a decimal.
Example
Calculation
Target: 95% Confidence, 5% RQL.
Risk: 0.05
p: 0.05
n = ln(0.05) / ln(0.95)
n = -2.996 / -0.051
n = 58.7 => 59
n = -2.996 / -0.051
n = 58.7 => 59
n
Sample Size
The number of parts to check.
β
Beta (Risk)
The Consumer's Risk (e.g., 0.05 or 5%).
p
RQL
The defect rate you want to detect (decimal).
Troubleshooting
Common issues when setting up inspection plans.
Sample Size is Too High
Check your RQL
If you enter an RQL of 0.01% (extremely rare defects), the math will demand thousands of samples to prove it. Is that realistic?
Adjust Confidence
Do you really need 99% confidence for a cosmetic label? Dropping to 90% or 95% drastically reduces sample size.
Lot Failed. Now what?
Do NOT Resample
The most dangerous mistake is "sampling until you pass." If you found a defect, the statistical validity is gone. You must quarantine the lot.
100% Inspection
The only way to save the lot is to inspect every single part (100% sort) and remove the bad ones.
Expert Knowledge
Common Sampling Questions
What does "c=0" actually mean?
c=0 is shorthand for "Acceptance Number (c) equals Zero". It is a zero-tolerance plan. If you find even 1 defect in your sample, the math assumes the entire lot is suspect, and you must reject it.
Can I use this for variable data (measurements)?
No. This calculator is for Attribute data (Pass/Fail). Variable data (e.g., "5.2mm", "10.1kg") gives you more information, so you can use smaller sample sizes with a Variables Plan (ANSI Z1.9).
Why doesn't Lot Size (N) matter much?
Think of it as Tasting Soup. If the soup is stirred well (randomized), a single spoonful tells you if it's too salty. It doesn't matter if the pot is 1 gallon or 100 gallons; the spoon (sample) size remains the same.
If I find 1 defect, can I just re-sample?
Absolutely Not. This is called "Gambling until you win." If you found a defect, the statistical validity of the "Pass" is broken. Re-sampling doubles your risk of accepting a bad lot.
What is Consumer's vs. Producer's Risk?
Producer's Risk (α): The chance we reject a Good lot. (The factory is sad, waste of money).
Consumer's Risk (β): The chance we accept a Bad lot. (The customer is sad, safety risk).
c=0 plans prioritize reducing the Consumer's Risk.
Verified Expert
Disclaimer: This tool is for informational and educational purposes only. Calculations are based on standard formulas but may not account for unique business variables. We do not accept liability for decisions made based on these results.