# Sampling plan for foreign objects

### #1 Lar

Lar

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Posted 24 May 2011 - 05:45 AM

Hello All,

I'm fairly new to this, so sorry if it has been covered before.

I was wondering if there is any statistical evidence out there for how much you should sample your batch if you detect a foreign object in your process. For example, if you produced 20 000kg of sauce which was packaged in 400 x 50KG containers. Upon visual inspection a "a piece of small cardboard" was found in one of the containers. How many containers would you then inspect to be confident that no other containers or at least 95% confident that no other containers contained any pieces of cardboard? Or would you simply dump all your product.??

Is there any evidence of sampling plans available?

Thanks

### #2 Charles.C

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Posted 24 May 2011 - 11:44 PM

Dear Lar,

I am no statistician but I suspect this is similar to the micro. problem of assuring by random sampling that a lot of food units has zero salmonella.

If you equate yr problem to the simple, general, situation where you have a certain percentage of “defective” containers in a batch, the equation involved is of the form

P = 1-(1-d/100) sup^n^

Where "P" is the probability of getting at least one defective unit in the sample, “d” is the percentage of defective units in the batch sampled and “n” is the number of packing units in the sample.

Approx, for P = 95 pct, n = (300/d)

(to state it another way, if you take the above sample size, n, and find no defectives, there is a 95% probability that there are less than d% defectives in the lot)

I’m afraid you hv a difficult sampling situation. The problem of course is the very low value of “d”.

I hv attached a table below to illustrate use of above equation -

Rgds / Charles.C

PS welcome to the forum !

Kind Regards,

Charles.C

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