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Introduction to Sampling(SQC)

Introduction to Sampling(SQC). What is sampling? What is an acceptance sampling plan? Attribute Type and Variable type sampling plans?. Introduction to Sampling:Mathematical Review. Binomial distribution:.

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Introduction to Sampling(SQC)

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  1. Introduction to Sampling(SQC) • What is sampling? • What is an acceptance sampling plan? • Attribute Type and Variable type sampling plans?

  2. Introduction to Sampling:Mathematical Review Binomial distribution: If 4 samples are chosen from a population with a defect rate = .1, what is the probability that exactly 1 out of 4 is defective? At most 1 out of 4 is defective? More than 1 is defective? P(x) = n choose x =

  3. Probability Distributions • Poisson:  = np • Poisson approximation to the binomial: can apply if n large and p small. • “Poisson is our friend” • If we sample 50 items from a large lot, what is the probability that 2 are defective if the defect rate (p) = .02? What is the probability that no more than 3 defects are found out of the 50?

  4. Probability Distributions (2) Hypergeometric Distribution: • This distribution is used when sampling from a small population. It is used when the lot size is not significantly greater than the sample size. (Can’t assume each part is independent). • A lot of 20 tires contains 5 nonconforming ones. If an inspector randomly samples 4 items, what is the probability of 3 nonconforming ones?

  5. N n Number Conforming Accept or Reject Lot Design of Lot-by Lot Sampling Plans Specify the plan (n,c) given N: for a lot size N, determine the sample size n, and the acceptance number c. (Reject lot if number of defects > c.) Specify course of action if lot is rejected.

  6. Definitions: • Type I error—The probability that something good is mistakenly judged as defective. • Type II error—The probability that a defective item or nonconforming lot is accepting as being “good” or nondefective. • Producer’s Risk—Risk of rejecting a “good lot.” This is a Type I error. • Consumer’s Risk—Risk of accepting a “poor lot.” This is a Type II error.

  7. Definitions AQL (Acceptable Quality Level) -- the maximum percentage of nonconforming items in a batch that can be considered acceptable. • LQL (Limiting Quality Level) – percentage of nonconforming items in a lot for which the consumer wishes the probability of acceptance is a specified low value. Also know as “unacceptable quality level.”

  8. Example: Lots of size N = 1000 fuses are inspected using an (50,3) sampling acceptance plan. Usually, the defect rate is 3% but occasionally there is a bad batch that has a 6% defect rate. • What is the producer’s risk of this sampling plan? • What is the consumer’s risk of this sampling plan? • What if the plan was changed to (50,2)? What would the relative change be between the consumer’s and producer’s risk?

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