# Probability analysis

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Viewing 7 posts - 1 through 7 (of 7 total)
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• #30750

NightCrawler
Participant

Does anyone know the formula for probability analysis?
To figure out the probability of someone picking a defective part out of a bin of 5 parts with 3 being defective.

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#80506

RSloop
Member

NightCrawler,
The Hypergeometric Probability Distribution is used when samples are taken (without replacement) from a finite population.
I can’t paste the formula here, but if you’d leave an email I’ll be glad to send it to you.
Regards,
Rick

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#80507

Gabriel
Participant

It is true! The hypergeometric distribution can help. But if the sample size is 1, you don’t need to care about the hyper….(etc, etc, etc.).
The distribution of results in this sampling has only two values: all good (i.e. the only part you picked is good) with a 2/5 (40%) of chance, or all bad (i.e. the only part you picked is bad) with a 3/5 (60%) of chance.
Now, if you had 100 parts, 30 of which are bad, and you want to know the probability of picking let’s say 10 of fewer bad parts in a sample of let’s say 50 parts, then go to the hyper….
Both approches assume that the probability of picking one specific part is the same for any the parts. If, for example, bad parts are more likely to be chosen, then nothing of this work.

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#80510

RSloop
Member

Good answer Gabriel and a good point about the probability of a good sample or bad sample being the same.
Rick

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#80531

NightCrawler
Participant

Please send the formula to [email protected]

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#80623

Thomas C. Trible
Member

Example Problem: Lots of 40 components each are called acceptable if they contain no more than 3 defectives. The procedure for sampling the lot is to select 5 components at random and reject the lot if a defective is found. What is the probability that exactly 1 defective is found in the sample if there are 3 defectives in the entire lot? Solution: Use the hypergeometric distribution…h(1;40,5,3)=(3 choose 1)X (37 choose 4)/(40 choose5) = 0.3011Sorry – I can’t use equation editor with this post… (3 choose 1) would be 3!/1!(3-1)! I think you can work backwards to determine the formula…

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#80629

rams
Participant

Agree that hypergeometric is used in this situation.
But what if you apply it to high volume production with let’s say a lot size of 5000 and above?  I had problems using the hypergeometric function in the excel software as it is somewhat limited to a certain factorial value (hypergeometric uses the factorial function).
My solution ? For very high lot sizes, I simply used the binomial distribution which assumes proby of a defective is constant (sampling with replacement); or I use the poisson distribution to estimate the binomial distribution which I usually do.
Not sure if I violated some assumptions or principles.
Rams

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