# How do I find a target standard deviation for my own testing given a confidence level, a mean, and bounds for the interval?

I'm working on a project involving a couple of material dispensers, and the customer we're designing them for has asked us to keep the output of the dispensers within a set range 95% of the time. I'm struggling with the statistics aspect of tuning the dispenser to get toward this output.

Basically I need to find a target metric (feels like standard deviation is the right metric here) and see if the tech we've developed can even meet that metric at all or if we need to re-evaluate and start over. Where would I get started on this? Do I need more information to calculate the target standard deviation? Am I going about this the wrong way?

The easy way would be to just test the system a million times and see if the error rate is acceptable, but this doesn't have a set endpoint and requires a tremendous amount of measurement with no real end in sight.

Thanks very much,

-G

• This might be a Mathematics SE question but I do appreciate the fact there may be a more practical engineering approach. I'm not sure what the math guys know but they might know a way to extrapolate what you need from what you have or they may go down an impractical theoretical rabbit hole. Nov 18, 2022 at 5:55
• I suppose the brute force way is to have a shadow dispenser where if the contents of the the hidden internal dispenser measure out of bounds, to just return the contents back it the machine stock and try again, only passing the contents to the external dispenser when it measures correctly. Or to build it in a way where it literally can't dispense the wrong amount short of a mechanical failure but that depends on the contents (for example over filling a powder cup and then swiping the top to remove the excess). Nov 18, 2022 at 6:07
• Post on Cross Validated - that's a statistics stack... Nov 18, 2022 at 7:01
• The usual statement would run more like 'we need to be 99% confident that 95% of the product meets the defined spec.' Designing a new process to meet a given confidence interval is tricky, whereas if you have the plant up and running you can start a SPC run chart. Dec 19, 2022 at 1:56
• Check out Weibull charts. Dec 20, 2022 at 11:35