What is truth? A practical guide to comparing reliability equation answers to simulation results

We found that our endeavor to resolve the absolute true MTTF of a simple system to be both enlightening and far more difficult to achieve than ever thought possible. Determining truth so that a sound foundation from which accurate comparative analysis between mathematical and simulation techniques can be conducted, is a difficult journey with many potential pitfalls. The profound conclusions of this simple exercise will surprise many of the most seasoned reliability experts as well as provide a roadmap to how best to compare two or more reliability methods. Our playful paper will show that although mathematical derivations can accurately solve a few textbook type problems, only simulation has the muscle to solve the truly interesting reliability problems.