FIT / APPLIED MATHS
PolytechnicRound 1/6Score 0
Quality Control
Acceptance sampling
20 parts200 parts
0 defects20 defects
Sampling decision
Accepting a sample does not prove the entire batch is defect-free.
Operating-characteristic curve
Good batch
Defect rate 1%
Must accept ≥95%
—
Bad batch
Defect rate 8%
Must reject ≥90%
—
No experimental samples yet.
Choose a sampling plan that meets both requirements.
The maths
Assume independent defects with constant defect probability p. This is a binomial approximation to large-lot sampling.
Let X be the defects in n inspected parts: X ~ B(n,p).
Probability of accepting a batch: Pₐ(p) = P(X ≤ c) = Σ from x = 0 to c of C(n,x)pˣ(1−p)ⁿ⁻ˣ.
Probability of rejecting a batch: Pᵣ(p) = 1 − Pₐ(p).
An OC curve plots Pₐ against the true percentage of defective parts. It is calculated exactly under the binomial model using recurrence, without Monte Carlo error.