Operations · Original fictional case
Combine defect counts across unequal inspection batches
Two inspection batches have different sample sizes. Produce the overall defect rate and identify which batches cross a stated internal review trigger.
Related work: Industrial Production Managers · O*NET task 39.
Your source data
| batch | inspected units | defective units |
|---|---|---|
| A | 100 | 5 |
| B | 900 | 9 |
The rules
- Each inspected unit is counted once, and defective_units counts units rather than the number of defects.
- Overall rate = total defective units ÷ total inspected units. Do not average batch percentages equally.
- Flag a batch only when its own defect rate is greater than 2%. This is a fictional review trigger, not an acceptance sampling standard.
A method you can reuse
- A has a 5% defect rate and B has a 1% rate. Their sample sizes are 100 and 900 respectively.
- Pool counts: 14 defective units out of 1000 inspected gives 1.4%. The unweighted average of 5% and 1% would be 3%.
- Flag A for review. The overall rate is below 2%, but it does not erase the higher observed rate in that batch.
A common wrong turn
Counting defect occurrences instead of defective units can produce a rate above 100% and a different measure entirely. Keep the numerator definition explicit.
Use it in a handoff
A small observed sample is not a production guarantee. Keep inspection scope, batch sizes and the review rule attached to the report.
Check your calculation
Enter numbers without currency or percent symbols. A matching result confirms this exercise’s calculation; keep the method in your review note.
See the worked answer
Total inspected units: 1000
100 + 900 = 1000.
Pooled defect rate (%): 1.4
14 / 1000 × 100 = 1.4%.
Inspected units without a defect: 986
1000 − 14 = 986.
Batches above the review trigger: 1
A is above 2%; B is below it.
Source and practice material
Occupational context uses the O*NET® 31.0 Database from the U.S. Department of Labor, Employment and Training Administration, under CC BY 4.0. View the occupation.
Skill Workbench selected and adapted the occupational information and added its own fictional cases, calculations, guidance and worksheets. USDOL/ETA has not approved, endorsed or tested these additions. O*NET® is a trademark of USDOL/ETA.