Use case 2 · Acceptance sampling

Sampling what a vendor sends in the plan's name

The pattern

A template error at a vendor repeats in every notice until someone at the plan reads one. The question is how many to read.

Question: How many vendor notices should the plan read each week?
Lane: Delegated vendor
Basis: Standard practice

What METRIS does

Draw a random weekly sample of each vendor's notices and check them against plan rules
Size the sample to the error rate the plan cannot tolerate
Report errors per vendor and template, and the members affected before detection

Chance one weekly sample catches the error

Exact calculation · assumed parameters

Reading 59 notices a week gives a 95% chance of catching a 5% error rate; a 1% rate needs 299. Exact binomial probabilities.

Method

P(detect in one week) = 1 − (1 − p)^n n needed for 95% = ⌈ ln 0.05 / ln(1 − p) ⌉ expected affected = V · p / P(detect)

Weekly volume (V): 5,000 notices
Error rates (p): 1%, 3%, 5%, 10%
Sample (n): 5 to 300 a week
Detection: At least one wrong notice in the sample

Reading notices at random is cheap; reading the right number is the difference between about 150 affected members and about 1,000.

Members affected before detection

Exact calculation · assumed parameters

With 5,000 notices a week and 3% wrong, reading 10 a week lets about 571 members get a wrong notice before detection; reading 100 cuts it to 157. Past about 100 the gain flattens.

Reproducibility

Closed-form binomial calculation, treating each read as independent (a close approximation when the sample is small next to weekly volume); no random draws. Python with NumPy 2.5.3 and SciPy.

Sources

This pattern is not based on any single record. Its figures come from the model stated above.

Study design and analysis: Suneeta Modekurty, SANJEEVANI AI

A statistical study of a pattern, not of any event. It identifies no organization or person. Simulated figures use synthetic data; published figures are industry-wide.