Hi, We are in a process to create our incoming raw material inspection procedure. We are planning to use ISO 2859 sampling by attributes scheme.
At we perform according to the international standard ANSI ASQC Z1.4 - ISO 2859 - MIL STD 105E. Our inspectors inspect your productions directly on site according to an established protocol by our supervisors and according to our clients requirement. In order to establish how many pieces/products will be inpected by our employees, we use the tables provided below. AQL is a method allowing to estimate if a production batch should be accepted or rejected by considering a sampling operated on a random selected part of this production. In order to learn how this method determines how many pieces are selected, let's work on an example: Considering a production of 10 000 units.
1/ First you have to know that an unit is the smallest element you consider on a production. 2/ In order to know how many units will be selected you have to choose a general inspection level. A general inspection level involves the accuracy used to led the inspection of your product. Most of the importers use General Inspection Level II to inspect a batch of product and Special Inspection Levels are reserved for special test led on products (such as torn test, high pot test, strength test, etc.).
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So now, let's consider 10 000 units ordered by an importers who chosse General Inspection levels II. In the table 1 you get L as sampling size code letters. Now by reporting this letter in the table 2, you get 200, which is how many pieces have to be inspected over 10 000 to represent statistically the quality of the batch of 10 000 piecs.
Stuart, The calculation for probability of defects within a lot of 100 pieces, a sample of 20 and 0 defects found is based on the Hyoergeometric Probability Distribution, since the lot is finite and the random sample is taken without replacement. The formula for finding the probability 'P' of 'd' defects in a sample of size 'n' from a lot of size 'N' is: P(d) = 'Combination of all defective units' multiplied by the 'Combination of all good units' divided by the 'Combination of all units' An easier method of finding the probabilities would be to use the Operating Characteristic curve (OC curve) for the sampling plan you are using. In the sampling plan find the 'Code Letter' for your universe of 100 and an Inspection II.
Find the OC curve for that code letter. The graph will have curves for various AQL's.
The 'x' axis is the percent defective of the lot and the 'y' axis is the probabilit of acceptance. Using the intersect of horizontal and vertical lines to the curve you can determine the probability of acceptance of a lot based on various percent defectives. In essence, for each percent defective you can look at the probability of accepting the lot based on your smapling result. A problem inherent with Operating Characteristic curves is that most are based on an assumption of an 'infinite' lot rather than the 'finite' lot size as you have. The curves therefore are not based on hypergeometric probabilities although the Poisson or binomial probability distributions often give acceptable results. There is an excellent discusion on sampling plans in 'Statistical Quality Control' by Grant and Leavenworth, ISBN 0-07-114248-7. There are also some good referemces on the web: has a good description of how a double sampling plan is created and therefore some insight into the problems you may run in to.
I hope this addresses your question adequately.