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Model

Rows a sample needs to see a rare defect

Sampling is cheapest exactly where it is weakest: the expensive defects are the rare ones.

Prevalence
the share of rows with the defect
Miss probability
chance of seeing it zero times (confidence 1 − β)

Recurring principle: Absence is not evidence

How it behaves

One input on the horizontal axis, the others held fixed.

95% confidence99% confidence
Data table
Rows needed to see a defect at least once, by prevalence
Prevalence pseriesRows to sample
095% confidence30M
095% confidence25.2M
095% confidence21.2M
095% confidence17.8M
095% confidence15M
095% confidence12.6M
095% confidence10.6M
095% confidence8.94M
095% confidence7.52M
095% confidence6.33M
095% confidence5.33M
095% confidence4.48M
095% confidence3.77M
095% confidence3.17M
095% confidence2.67M
095% confidence2.25M
095% confidence1.89M
095% confidence1.59M
095% confidence1.34M
095% confidence1.13M
095% confidence947K
095% confidence797K
095% confidence671K
095% confidence564K
095% confidence475K
095% confidence399K
095% confidence336K
095% confidence283K
095% confidence238K
095% confidence200K
095% confidence168K
095% confidence142K
095% confidence119K
095% confidence100K
095% confidence84.4K
095% confidence71K
095% confidence59.8K
095% confidence50.3K
095% confidence42.3K
095% confidence35.6K
095% confidence30K
095% confidence25.2K
095% confidence21.2K
095% confidence17.8K
095% confidence15K
095% confidence12.6K
095% confidence10.6K
095% confidence8.94K
095% confidence7.52K
095% confidence6.33K
0.00195% confidence5.33K
0.00195% confidence4.48K
0.00195% confidence3.77K
0.00195% confidence3.17K
0.00195% confidence2.67K
0.00195% confidence2.25K
0.00295% confidence1.89K
0.00295% confidence1.59K
0.00295% confidence1.34K
0.00395% confidence1.13K
0.00395% confidence947
0.00495% confidence797
0.00495% confidence671
0.00595% confidence564
0.00695% confidence475
0.00895% confidence399
0.00995% confidence336
0.01195% confidence283
0.01395% confidence238
0.01595% confidence200
0.01895% confidence168
0.02195% confidence142
0.02595% confidence119
0.0395% confidence100
0.03695% confidence84.4
0.04295% confidence71
0.0595% confidence59.8
0.0695% confidence50.3
0.07195% confidence42.3
0.08495% confidence35.6
0.195% confidence30
099% confidence46.1M
099% confidence38.7M
099% confidence32.6M
099% confidence27.4M
099% confidence23.1M
099% confidence19.4M
099% confidence16.3M
099% confidence13.7M
099% confidence11.6M
099% confidence9.73M
099% confidence8.19M
099% confidence6.89M
099% confidence5.8M
099% confidence4.88M
099% confidence4.1M
099% confidence3.45M
099% confidence2.91M
099% confidence2.44M
099% confidence2.06M
099% confidence1.73M
099% confidence1.46M
099% confidence1.23M
099% confidence1.03M
099% confidence867K
099% confidence730K
099% confidence614K
099% confidence517K
099% confidence435K
099% confidence366K
099% confidence308K
099% confidence259K
099% confidence218K
099% confidence183K
099% confidence154K
099% confidence130K
099% confidence109K
099% confidence91.9K
099% confidence77.3K
099% confidence65K
099% confidence54.7K
099% confidence46.1K
099% confidence38.7K
099% confidence32.6K
099% confidence27.4K
099% confidence23.1K
099% confidence19.4K
099% confidence16.3K
099% confidence13.7K
099% confidence11.6K
099% confidence9.73K
0.00199% confidence8.19K
0.00199% confidence6.89K
0.00199% confidence5.8K
0.00199% confidence4.88K
0.00199% confidence4.1K
0.00199% confidence3.45K
0.00299% confidence2.91K
0.00299% confidence2.44K
0.00299% confidence2.06K
0.00399% confidence1.73K
0.00399% confidence1.46K
0.00499% confidence1.23K
0.00499% confidence1.03K
0.00599% confidence867
0.00699% confidence730
0.00899% confidence614
0.00999% confidence517
0.01199% confidence435
0.01399% confidence366
0.01599% confidence308
0.01899% confidence259
0.02199% confidence218
0.02599% confidence183
0.0399% confidence154
0.03699% confidence130
0.04299% confidence109
0.0599% confidence91.9
0.0699% confidence77.3
0.07199% confidence65
0.08499% confidence54.7
0.199% confidence46.1

Worked examples, recomputed

Every number the mechanisms quote for this relationship is recomputed from it, so none of them disagrees with it.

Where it appears

Each mechanism states it in its own names. The general symbol each name stands for is shown with it.