Lect 19 -20.pdf

# Lect 19 -20.pdf - Sampling Plans Supplier 100 Insp 100 Insp...

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Sampling Plans

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Customer Supplier 100% Insp. 100% Insp. Customer Supplier 100% Insp. Sample Insp. Customer Supplier Sample Insp. SPC.
A procedure for sentencing incoming batches or lots of items without doing 100% inspection What is acceptance sampling?

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Purpose of acceptance sampling? Determine the quality/reliability level of parts in an incoming shipment or at the end of production and judge whether quality/reliability level is within the level that has been predetermined.
The general approach N (Lot) n Count Number Conforming Accept or Reject Lot Specify the sampling plan For a lot size N, determine the sample size (s) n, and Select acceptance criteria for good lots Select rejection criteria for bad lots Accept the lot if acceptance criteria are satisfied Specify course of action if lot is rejected

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What's a good and bad lot ? Acceptance quality level (AQL) The smallest percentage of defectives that will make the lot definitely acceptable. A quality level that is the base line requirement of the customer RQL or Lot tolerance percent defective (LTPD) Quality level that leads to maximum acceptable consumer’s risk
d A c ? Reject lot Yes Accept lot Do 100% inspection Return lot to supplier Inspect/test all items in the sample Defectives found = d No Take a randomized sample of size n from the lot N Example : Single Sampling procedure

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Sampling plans are based on sample statistics and the theory says that since we inspect only a sample and not the whole lot, there is a chance of making an error. This means, given an overall probability of occurrence of an event, a sample (which is smaller than the population) will have its own probability of experiencing that event.
Example 100 Lots of size 5000 and a known quality level of 1% defectives were taken. One sample of size = 100 was drawn from each lot. If it was decided that if sample contained > 1 defective units, it should be rejected. In this case the acceptance number is 1

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Simulation Example Each square is a lot of size 5000. Sampling will be done using a sample size of 100 and number of defectives will be recorded
0 3 0 0 1 2 2 0 1 1 1 0 0 0 2 2 0 0 0 1 1 1 0 1 0 0 1 0 0 0 1 2 0 3 1 0 0 0 3 0 1 1 0 0 1 1 0 0 2 2 1 0 0 0 0 2 1 0 0 2 2 1 1 0 1 0 0 1 2 1 0 0 0 1 0 2 1 2 1 0 1 1 1 3 0 0 4 0 2 2 0 1 1 1 1 0 0 0 3 1 Simulation Example This is an output from a simulator which is set to produce defectives in samples from lots with 1 % defectives We are supposed to reject lots where the sample contained more than 1 defective units

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0 3 0 0 1 2 2 0 1 1 1 0 0 0 2 2 0 0 0 1 1 1 0 1 0 0 1 0 0 0 1 2 0 3 1 0 0 0 3 0 1 1 0 0 1 1 0 0 2 2 1 0 0 0 0 2 1 0 0 2 2 1 1 0 1 0 0 1 2 1 0 0 0 1 0 2 1 2 1 0 1 1 1 3 0 0 4 0 2 2 0 1 1 1 1 0 0 0 3 1 Simulation Example No. of lots rejected = 21 We are supposed to reject lots where the sample contained more than 1 defective units
We need to consider two types of errors that result in wrong decisions Type 1 Error No Error No Error Type 2 Error Reject Accept Good lot Bad lot T R U T H DECISION

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TYPE I ERROR = P (reject good lot) or Producer’s risk 5% is common TYPE II ERROR = P (accept bad lot) or Consumer’s risk 10% is typical value Errors and Risks
Producer’s & Consumer’s Risks
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• Fall '17
• Makarand Kulkarni

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