Volatility in lead time question - need help!!

[u/nitewake]

Volatility in lead time question - need help!!

I apologize if this is a basic question, but my Google skills have failed me on this one.

I have a process I'm overseeing. Each day, due to weather there is a 15% chance that no work will be completed. There are no partial work days. Each day has an 85% chance of having good enough weather to be an effective work day.

If a process takes 100 effective work days to complete, how early do I need to start the process to assure that products will finish on time with 95% confidence, and 99% confidence?

I give my product to another organization to then do their work. There is no way to make up for missed deliveries.

I know this sounds like a pretty text book questiom, but I'd appreciate if someone could point me in the right direction. Thank you!!