How Many Parts to Sample for a Complete Set with 95% Confidence?

[Bandit127]

I could do with some help here about a problem I had at work today.

I have a process that dumps 8 parts in a bin every cycle. Each part is numbered, 1 to 8. (It is a big bin and it will contain an equal quantity of each number).

I need to measure one part of each number, so I need to grab a sample of parts from the bin.

How many parts do I need to pull out of the bin before I have a 95% chance of getting at least one of each number? (My guess was 40 parts, but in two samples of 40 parts I had two numbers missing from each sample. Loads of 5s but no 1s for example).

So, I worked out that the probability of getting 1 to 8 in the first 8 moulds is 8!/8⁸ or about 0.0024.

But there I got stuck on how that probability changes with the next set of 8 parts I pull from the bin. And so on until I have a ~95% chance of getting them all.

 

[berkeman]

I could do with some help here about a problem I had at work today.

I have a process that dumps 8 parts in a bin every cycle. Each part is numbered, 1 to 8. (It is a big bin and it will contain an equal quantity of each number).

I need to measure one part of each number, so I need to grab a sample of parts from the bin.

How many parts do I need to pull out of the bin before I have a 95% chance of getting at least one of each number? (My guess was 40 parts, but in two samples of 40 parts I had two numbers missing from each sample. Loads of 5s but no 1s for example).

So, I worked out that the probability of getting 1 to 8 in the first 8 moulds is 8!/8⁸ or about 0.0024.

But there I got stuck on how that probability changes with the next set of 8 parts I pull from the bin. And so on until I have a ~95% chance of getting them all.

So I have to ask -- why can't you look into the bin and select 8 parts that have different numbers? Why do you have to pull a part out of the bin before looking at the number? Seems like a very inefficient way to design a process, IMO.

 

[Stephen Tashi]

Does this problem amount to the coupon collectors problem? http://en.wikipedia.org/wiki/Coupon_collector's_problem