Probability
Defect Rate Probability Calculator
Model lot defect counts with a binomial distribution, calculate action-threshold probability, and split per-unit defects into detected and missed paths.
Per-unit defect probability-
Expected defects in lot-
Probability lot reaches action threshold-
Probability lot contains no defects-
Probability a random unit is defective and detected-
Probability a random unit is defective but missed-
Expected undetected defects in lot-
Decision view
Defect-count threshold, lot tiles, and inspection escape path
Defect-count threshold, lot tiles, and inspection escape pathA discrete count distribution marks the action region while lot tiles distinguish expected detected defects from escapes.
Exact scenario comparisonIndependent defect probability per unit (%) changes while all other entered assumptions remain constant.
| Independent defect probability per unit (%) | Per-unit defect probability | Expected defects in lot | Probability lot reaches action threshold | Probability lot contains no defects | Probability a random unit is defective and detected | Probability a random unit is defective but missed | Expected undetected defects in lot |
|---|
How to use Defect Rate Probability Calculator
- Enter lot size and an independent per-unit defect probability.
- Set the count that triggers action.
- Enter validated defect-detection sensitivity.
Calculator guide
Understanding Defect Rate Probability Calculator
A defect-rate calculation has two layers: how many defects the process creates and how many inspection detects. Mixing them hides escaped defects.
Detailed calculation process
Detailed lot defect and inspection calculation
The default lot has 80 units, 2% independent defect probability, a three-defect action threshold, and 95% detection sensitivity.
General formula: E[D]=npP(D≥k)=1-Σ[i=0..k-1]C(n,i)p^i(1-p)^(n-i)p_detect=p*sp_escape=p(1-s)E[escape]=np_escape The lot threshold depends on produced defects. Sensitivity then partitions those true defects into detected and missed paths.
What each symbol means
Worked substitution with the default inputs
The default lot expects 1.6 defects, has about a 21.56% action probability, and averages 0.08 undetected defects.
Worked situations
Practical examples
- The default lot expects 80×2%=1.6 defects.
- A 95% sensitive inspection leaves a 0.1% per-unit escape probability and 0.08 expected escapes per lot.
Better inputs
Useful tips
- Stratify by defect mode when sensitivities differ.
- Use clustered or beta-binomial models when defects are correlated.
- Separate false positives from sensitivity in a full inspection model.
Before relying on the result
Limitations and common mistakes
- Defects are assumed independent with a constant rate.
- Specificity and false-positive inspection decisions are omitted.
- Expected escapes are an average, not a guaranteed fractional count.
Reference
Key terms
- Action threshold
- Defect count at or above which the lot triggers action.
- Sensitivity
- Probability inspection detects a truly defective unit.
- Escape
- A true defect missed by inspection.
Important note
Use validated process data, sampling plans, measurement-system analysis, defect-mode sensitivities, and applicable quality standards before release decisions.
Frequently asked questions
Why is expected defect count not the most likely count?
Expectation is a long-run average and can fall between discrete counts.
Does 95% sensitivity mean 5% of all units escape?
No. Five percent of truly defective units escape.
What about false rejects?
They require inspection specificity, which this model does not include.