We were tasked to provide Safety Support for the Marine Corps GBOSS project. The Logistics team was required to insure that our product had a Mean-Time-Between-Failure (MTBF) below a certain threshold. They used statistics to show that we would need to conduct 1000s of hours of testing. Since this was a complex and expensive system, this approach was going to require extending the schedule and adding $100,000s to the project cost.
Although outside our task scope, we took a closer look at how the statistics were used and what they were based on. We traced this back to the original requirements document, which specified what the MTBF goal was and saw that the testing recommendation missed the intent of the MTBF requirement.
We showed the Project Management that a better understanding of the true reliability goals would reduce the resulting test time by an order of magnitude, saving the Program many $100,000s.