Lower confidence bound on the percentage improvement in comparing two failure rates

It is often necessary to determine whether a design change in a product has actually improved its failure rate, and to compute a lower confidence bound on the percentage of failure rate improvement affected by the change. It is shown that such a bound can be computed based on certain test data. The main result is a special case on an equivalent result derived in Lehmann (1959) for hypothesis testing and used extensively in applied statistics. However, it is not well known in its confidence interval form, nor is it extensively reported in reliability methods books, and its derivation is important in reliability testing