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Acceptance Sampling

Acceptance Sampling. Items are sold as a group ( lot ) by a producer to a consumer Each lot has a certain fraction p of defective items Consumer will only accept lot if p is small How should consumer decide? A: Inspect a sample from lot Not currently popular QC method .

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Acceptance Sampling

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  1. Acceptance Sampling • Items are sold as a group (lot) by a producer to a consumer • Each lot has a certain fraction p of defective items • Consumer will only accept lot if p is small • How should consumer decide? • A: Inspect a sample from lot • Not currently popular QC method

  2. Simple sampling plan • Choose a sample size n and critical value c • If sample has >c defectives, reject sample • P(A) = P( X c) depends on c,n,p,N • Worksif n <<N, (rule of thumb n < 0.5 N) • Does not hold if n is large relative to N

  3. Sampling without replacement • Lot has N items, Np defective, N(1-p) good • P(1st item is defective) = Np/N = p • P(2nd item is defective) depends on 1st item • Not i.i.d. trials, binomial model does not hold • P( X c) can be calculated using combinatorics

  4. Hypergeometric Distribution • An urn contains N balls, M red, rest blue • You select n balls as SRSWOR • What is the chance k are red? • Hypergeometric used in estimating wild-life populations by capture-recapture method

  5. Acceptance probability • An acceptance plan is a choice of n and c • P(A) cannot be calculated in practice • How do we choose a sampling plan? • A: look at an OC curve

  6. OC Curve • Is this a good OC curve? • What does an ideal OC curve look like ?

  7. 1 P(A) 1 AQL Optimising the OC curve • Decide how close to ideal you want to be • Consult a table of sampling plans for n and c • More sophisticated sampling plans exist

  8. Modelling rare events • # of misprints in a page of a book • # of radioactive emissions from a block of uranium in a minute • Binomial expt. n large, p small • If np , then • This limit is known as the Poisson distribution

  9. =3 Poisson distribution • l is known as the rate parameter • Poisson distr. also used to model events over time • X(t) = # events upto time t • X(t) is a stochastic(random) process

  10. Poisson process Poisson process (rate = l) P(N(t)=k) = (lt)k e-lt / k!

  11. Telephone traffic • Traffic at exchange at a rate of 500/hour • What is chance of no calls is 2 mins? • Avg no. of calls in 10 min

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