I could. But that would be inappropriate here. The lower bound of any such interval would be astonishingly close to a failure rate of 0, while the maximum likelihood estimator is itself fairly close to 0. Therefore any reasonable set of priors usually puts you in the upper tail.

For instance one such interval has a MLE of an engine failure rate of 2.78%, a lower bound of 0.1% and an upper bound of around 15%. (Corresponding rocket failure rates range from 1 in 10 million to about 9.9%.)