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Say I have a factory that produces bottles of salt water, and there are two processes. One adds some water to a bottle and the other adds some salt.

I have stats on each process. ie. a sample of how much water added to a bottle (litres), a sample of how much salt added to a bottle (grams). I am interested in the statistics of concentration (grams/litre). I have no way of taking a sample final concentration once the process is complete.

Can I combine the measured samples to get some sort of derived distribution, I can do statistical work on? In the end I would like to build a tolerance interval of bottle concentration.

I have thought about doing a Monte-Carlo simulation, where I randomly select a point from each sample, calculate the concentration, replace the points and repeat many times to get a derived concentration distribution. Is this flawed?

Thanks!

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    $\begingroup$ The most fundamental issue concerns the possibility of dependence between the two processes. What can you say about that? If you can assume independence, then the next issue concerns what you have: exactly which "stats" do you have or can you obtain? $\endgroup$
    – whuber ♦
    Commented Nov 18, 2021 at 15:04
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    $\begingroup$ If they are independant, and say that I have randomly recorded the amount of water added 100 times and the amount of alt added 100 times $\endgroup$
    – zsky3333
    Commented Nov 18, 2021 at 21:16

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