How to estimate the ideal sample size to validate failure rate in a process?

[#1]

Hello!

I have a factory process with a hypothesized failure rate of p=0.02, based on previous trials.

I would like to get the ideal sample size to validate if my process has a failure rate no larger than 0.02. How would you approach this?

Thanks in advance

[#2 · Accepted solution]

Hello @PValueEnemy,

For this specific question, I would use one of the Calculators available in "Help", "Sample Index".
If you go into Teaching ressources, there is a panel for Calculators, and there is one calculator named "Sample Size for Confidence Interval".

When you open it, you specify that you are interested in "Proportion" :

And then you'll have to fill some informations so that the calculation can be done. For your specific problem, you need to specify the confidence level required, the planned value, and the desired margin of error. Here as an example, as soon as all windows have been filled, I obtain the calculated sample size needed :

More infos here : JMP Student Subscription

I hope this will help you,

[#3]

Hi @PValueEnemy : In addition to the option provided by @Victor_G , you can try the following under DOE/Sample Size Explorers:

Then you'll see this.

You'll notice the required sample size depends on the number of failures in the sample.  These two methods are equivalent (though the input/output looks different); except for the fact that the calculator @Victor_G  suggested is based on the normal approximation, whereas this one is based on the exact (based directly on the binomial distribution rather than any approximation to the binomial distribution.) Clopper-Pearson interval.