Zero Acceptance (c=0) Sampling Plan Calculator
Zero acceptance number sampling plans, written c=0, accept a lot only if no defects are found in the sample. They are common in aerospace receiving inspection because they are simple and give a clear rejection rule. This calculator finds the sample size and shows the OC curve.
Your numbers
Defect rate you want to reject with high probability.
Compare your current sample size with the calculated minimum.
Your results
Uses the binomial model with acceptance number c=0, which is accurate for large lots and a good approximation otherwise. For small lots the hypergeometric distribution is exact. Follow the sampling plan required by your customer or contract.
OC curve: acceptance probability vs lot defect rate
Sweeps Actual lot defect rate from 0 to 20, holding your other inputs fixed.
Sampling rules at receiving
Want sample sizes set from supplier history in your ERP receiving screen? We can outline how it would work.
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How to use the calculator
Enter the lot size and the limiting quality, which is the defect rate you want to catch with high probability. Pick the consumer risk, the chance you are willing to accept a lot at that bad level. The calculator returns the smallest sample size and adjusts it for finite lots. Then enter the sample size you currently use and the real defect rate you expect to see. The calculator shows your consumer risk, the probability of accepting a lot at the actual defect rate, and the chart traces the whole OC curve from zero to twenty percent defective.
The math
With acceptance number zero, a lot is accepted only when every sampled unit is good. Under the binomial model, probability of acceptance equals (1 minus p) to the power n, where p is the lot defect fraction and n the sample size. The smallest n that holds consumer risk at beta for a limiting quality LTPD is the natural log of beta divided by the natural log of (1 minus LTPD), rounded up. For example, a 10 percent LTPD and 10 percent consumer risk needs 22 units. The finite-lot adjustment scales n down for small lots but remains an approximation.
- Pa = (1 - p)^n for c = 0
- n = ceil(ln(beta) / ln(1 - LTPD))
- Finite lot approximation: n / (1 + n / N)
Reading the OC curve
The OC curve falls steeply for c=0 plans. At a defect rate of 2 percent with 22 units, the probability of acceptance is about 64 percent, which means a lot with a real defect rate that low will often still be rejected. This is the price of zero acceptance: it protects the consumer strongly but penalizes good lots with small defect rates. If your supplier has a real defect rate well below the LTPD, a larger sample with c greater than zero can offer a better balance, but only if the contract allows it.
Common mistakes
A common error is quoting an AQL when using c=0 plans, since AQL and LTPD describe different points on the curve. Another is applying the calculated sample size to attribute checks of multiple characteristics without defining what counts as a defective unit. Finally, remember that sampling does not improve the lot: rejected lots need a defined disposition such as 100 percent sort or return, and the supplier needs corrective action.
Frequently Asked Questions
What does c=0 mean?
It means the acceptance number is zero. If any defective unit is found in the sample, the lot is rejected. If none are found, the lot is accepted. It is easy to apply and common in aerospace and defense.
How is this different from ANSI/ASQ Z1.4?
Z1.4 is indexed by AQL and lot size and typically allows an acceptance number above zero. A c=0 plan is designed from a limiting quality and consumer risk. Use whichever your customer or procedure requires.
Why is the finite lot value only approximate?
Sampling without replacement from a small lot follows the hypergeometric distribution, not the binomial. The adjustment here is a standard approximation. For small lots, use hypergeometric tables or software to confirm.
Can I use this for variables data?
No. This plan counts defective units, which is attribute data. For measured data, use a variables sampling plan or monitor the characteristic with capability analysis.
If you want sample size and lot disposition suggested automatically at receiving from supplier history in your ERP, we can help design that.
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Keep exploring
Free tools
- SAP QM Zero Acceptance Sample Size CalculatorFind how many units to inspect when the rule is accept on zero defects, for a given lot size, LTPD and consumer risk.
- Supplier Lot Acceptance Probability CalculatorCalculates the chance an incoming lot is accepted for a given supplier defect rate and sampling plan, and plots the operating characteristic curve.
- Microbial Sampling Plan Acceptance Probability CalculatorSee how likely a zero-tolerance sampling plan is to detect a contaminated lot, and how many samples you need for a target confidence.
ERP fixes and how-tos
- How to Create a Sampling Procedure in SAP QMCreate a sampling procedure and sampling scheme in SAP QM: QDV3, QDP1, sample types, valuation modes and how to assign them to inspection plans.
- How to create an inspection plan in SAP QM (QP01)Create an inspection plan in SAP QM with QP01: header, operations, master inspection characteristics, sampling procedure and material assignment, plus a plan report.
Guides
- SyteLine Inspection Plan Setup and Configuration GuideConfigure SyteLine inspection plans with test criteria, sampling rules, and measurement specs. Set up receiving, in-process, and final inspection plans in CloudSuite.
- The 90-Day AI Roadmap for Manufacturers: From Zero to Production AgentsA 90-day AI roadmap for manufacturers: week-by-week plan from first pilot to production AI agents inside your ERP, with milestones and budget guidance.
- Zero Trust Architecture for Manufacturing IT and ERPZero trust architecture for manufacturing IT: apply NIST SP 800-207 to ERP and plant systems, replace VPN with ZTNA, and phase a realistic 18-month roadmap.