## probability of failure in a multi-component system

I want to calculate the failure rate of a system that has multiple independent points of failure. If any one of these intermediate points fail then the entire system fails. I can determine the failure rates of the intermediate steps but am not sure how that can be extended to making any statements about the system as a whole.

For example, user A wants to send an email to user B. The outcome that I want to describe is that either user B receives the email or does not. The goal is to define some rate of success that describes how likely it is that user B will receive an email from user A. There are several intermediate steps in the process of sending the email such as one or more mail servers failing, routers not responding, power outages, floods, etc. Each of these intermediate steps has a known failure rate and as previously mentioned, it only takes one of these intermediaries to fail to prevent user B from receiving the email.

I was taking a Monte Carlo approach but was thinking that I may be missing a simpler and more fundamental approach to determining the likelihood of user B receiving that email. As you can tell, I’m not strong in stats so your help will be appreciated.

Thanks!