Calculator Form
Example Data Table
This example uses a c=0 plan with sample size 59. It shows how acceptance probability drops as defect rate rises.
| Defect Rate | Sample Size | Acceptance Number | Acceptance Probability | Detection Confidence |
|---|---|---|---|---|
| 0.5% | 59 | 0 | 0.7440 | 25.60% |
| 1.0% | 59 | 0 | 0.5527 | 44.73% |
| 2.0% | 59 | 0 | 0.3037 | 69.63% |
| 5.0% | 59 | 0 | 0.0485 | 95.15% |
Formula Used
Core c=0 rule: accept the lot only when the inspected sample contains zero defects.
Binomial approximation: Pa = (1 - p)n
Pa is the probability of acceptance. p is the defect proportion. n is the sample size.
Detection confidence: Confidence = 1 - Pa
Finite lot exact method: Pa = C(N - D, n) / C(N, n)
N is lot size. D is the estimated number of defectives in the lot. This page uses a conservative ceiling value for D when a finite lot method is selected.
Producer risk: alpha = 1 - Pa at AQL
Consumer risk: beta = Pa at LQL or RQL
AOQ approximation: AOQ = Pa × p × (N - n) / N
AOQ is useful when rejected lots are fully screened and corrected.
How to Use This Calculator
Choose Plan Design when you know AQL, LQL or RQL, alpha, and beta.
Choose Detection Confidence when you want the sample size needed to detect a target defect rate with a chosen confidence.
Use the binomial option for large lots. Use the finite lot exact option when lot size matters.
Enter the lot size. Add the relevant percentage inputs. Click calculate.
Read the recommended sample size and keep acceptance number at zero.
If you already inspected a sample, enter observed defects. The tool will return the c=0 lot decision.
Download the result as CSV or PDF for reporting, supplier reviews, and audit evidence.
Zero Defect Sampling in Quality Control
What Zero Defect Sampling Means
Zero defect sampling is a strict attribute inspection method. It uses an acceptance number of zero. That means the lot passes only when the sample contains no defectives. One defect causes rejection. This approach is simple to explain. It is also easy to audit. Many teams use it when failure costs are high.
Why Quality Teams Use c=0 Plans
Quality control managers often need faster screening than full inspection. A c=0 plan reduces effort while keeping the decision rule clear. It works well for incoming inspection, process checks, and final release reviews. It is especially useful when customers expect very low defect levels. Aerospace, electronics, medical supply chains, and critical assembly work often prefer strict acceptance logic.
How Risk Changes Under a Zero Acceptance Rule
The main tradeoff is risk balance. A c=0 plan usually lowers acceptance of poor lots quickly. That helps the customer. However, good lots can also be rejected if the sampling target is aggressive. This is the producer risk side of the decision. The consumer risk side measures the chance of accepting a poor lot. The best plan depends on the defect level you want to detect and the confidence you need.
How to Apply the Result
Start with the lot size and the defect rate assumptions. Then define either AQL and LQL targets or a direct detection goal. Use the calculated sample size as the inspection requirement. Randomly pull the sample. Inspect every selected unit carefully. If the sample shows zero defects, accept the lot. If the sample shows one or more defects, reject the lot or move to containment and corrective action.
Best Practice for Real Operations
Use c=0 plans with stable processes and trusted inspection methods. Pair them with supplier scorecards, trend charts, and root cause follow-up. Record each plan revision. Save the result sheet for audits. Most important, review whether your requested alpha and beta limits are realistic. Strict zero defect goals are powerful, but they should still match process capability and business risk.
FAQs
1. What is a zero defect sampling plan?
It is an acceptance sampling plan with c=0. The lot is accepted only when the inspected sample contains zero defects. One defect rejects the lot.
2. When should I use c=0 sampling?
Use it when defects are costly, safety matters, or customer expectations are strict. It fits high-risk products, critical parts, and strong incoming quality programs.
3. Why can producer risk become high?
Because a zero acceptance rule is severe. Even a good process with a very small defect rate can still produce a sample that contains one defective unit.
4. What is the difference between binomial and finite lot methods?
Binomial works well when the lot is large relative to the sample. Finite lot exact calculations are better when the sample is a meaningful share of the lot.
5. What do AQL and LQL mean here?
AQL is the quality level you still want to accept often. LQL or RQL is the poorer quality level you want to reject most of the time.
6. Can a requested c=0 plan be impossible?
Yes. Very strict alpha and beta targets can conflict under c=0. The calculator flags that case and suggests using different assumptions or detection mode.
7. What does detection confidence mean?
It is the chance that the sample will catch at least one defective item when the lot truly has the target defect rate you entered.
8. Why export CSV or PDF results?
Exports help with audit trails, supplier reviews, inspection packets, and internal approvals. They also make repeat calculations easier to document and share.