Understanding Acceptance Probability
Acceptance probability tells how likely a sampled lot will pass inspection. It is widely used in quality control, manufacturing, packaging, and supplier review. A sampling plan does not inspect every item. It tests a selected sample and accepts the lot when defects stay within the allowed count. This makes decisions faster while still giving measurable risk information.
Why This Calculator Helps
This calculator supports both common planning needs. You can estimate the chance that a lot passes at a stated defect rate. You can also compare producer risk at AQL and consumer risk at LTPD. The result helps teams judge whether a plan is too strict, too loose, or balanced. A small acceptance number lowers acceptance probability. A larger sample usually improves discrimination between good and poor lots.
Using the Results
The main value is the probability of acceptance, often called Pa. A high Pa means the lot is likely to pass. A low Pa means rejection is more likely. Rejection probability is simply one minus Pa. Expected defects show the average count expected in the sample. These values should be read with process knowledge. They do not prove every item is good. They describe risk under the selected statistical model.
Binomial and Finite Lot Models
The binomial model works well when the lot is large compared with the sample, or when items can be treated as independent. It uses the defect proportion directly. The finite lot model uses the hypergeometric distribution. It is useful when the lot size is known and the sample is a meaningful part of the lot. This model adjusts for sampling without replacement.
Good Practice
Choose sample size and acceptance number before inspection begins. Avoid changing limits after seeing results. Record the lot size, defect rate assumption, model, and calculated risks. Compare several plans before adopting one. A useful plan should protect customers while avoiding needless rejection of good production. The best setting depends on cost, safety, defect severity, and contractual quality rules. Use exported results for audits, supplier discussions, and process improvement reviews. When inspection data becomes available, compare actual sample defects with the expected value. Large differences may signal early process drift, counting errors, mixed lots, or changing supplier performance.