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Unformatted text preview: 1 INSE 6220 -- Week 12 Advanced Statistical Approaches to Quality • Acceptance Sampling • Final Exam Review Dr. A. Ben Hamza Concordia University 2 Acceptance Sampling • Why Acceptance Sampling and not 100% Inspection? • Testing is destructive • Cost of 100% inspection is high • 100% inspection is not feasible (require too much time) • If vendor has excellent quality history Advantages and Disadvantages of Sampling Advantages • Less expensive • Reduced damage • Reduces the amount of inspection error Disadvantages • Risk of accepting “bad” lots, rejecting “good” lots. • Less information generated • Requires planning and documentation 3 Acceptance Sampling Problem: • A lot (shipment) is received. • A sample is taken from the lot. • Some quality characteristic of the units in the sample is inspected. • On the basis of this inspection information, the lot is sentenced “accept” or “reject” Type of sampling plans • classification is by data type, variables and attributes • Based on the number of samples required for a decision: Single-sampling plans Double-sampling plans Multiple-sampling plans Sequential-sampling plans 4 Lot formation • Lots should be homogeneous. • Larger lots are preferred over smaller ones. • Lots should be conformable to materials-handling systems used in both supplier and consumer facilities. • Random Sampling Single Sampling plan • A lot of size N submitted for inspection. • Single sampling plan defines: Sample size, n Acceptance number, c • Operating Characteristic (OC) Curve To measure the performance of a sampling plan. The OC curve plots the probability of accepting the lot versus the lot fraction defective . Show the probability of a lot submitted, with certain fraction defective, will be either accepted or rejected. 5 OC Curve • Lot size, N large • # defective, d , in a random sample of size n will follow a binominal distribution with parameters, n and p . • The probability of acceptance is P (d c) ! ( ) 1 , 0, 1, 2, ..., !( )! n k k n P d k p p k n k n k ! (Accept lot) ( ) ( ) 1 !( )! c n k k a k n P P p P d c p p k n k OC Curve plots the probability of accepting the lot P a versus the lot fraction defective p (true proportion nonconforming) . Example: An apple producer has 500 baskets of apples, containing 20 each (10000 apples in the lot). A buyer wants to inspect 10 of the apples before accepting the lot (if 2 or less are bruised). That is n=10, N=10000, c=2. Suppose 20% of the apples are bruised, what is the probability of accepting such a lot?...
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