The CEO of the engine manufacturer wants to reassure customers. He promises that in the next month, there will not be multiple engine failures (no more than 1 failure).

Assume the probability of failure is exponential.

Question 1: The CEO asks you to calculate the probability that they are correct: What is the probability there will be no more than a single engine failure in the next month?

Note: Making promises to reassure customers and then asking to hear the numbers. This would never happen in the real-world, by the way.

The engine manufacturer above has observed that their engine control modules (ECM) fail as a direct function of how many hours they are active. The mean time between failures for the ECM is 50,000 operating hours. Accounting has determined that the company cannot profitably afford to pay for the repair of more than 12% of the ECM modules produced.

Question 2: What do you estimate to be the maximum acceptable warranty period (in operating hours) so that the company does not end up having to exceed the guidance for acceptable fraction of units repaired under warranty?