  Manufacturers are required to demonstrate products meet reliability targets.
A typical way to achieve this is with reliability demonstration tests (RDTs),
in which a number of products are put on test and the test is passed if a
target reliability is achieved. There are various methods for determining the
sample size for RDTs, typically based on the power of a hypothesis test
following the RDT or risk criteria. Bayesian risk criteria approaches can
conflate the choice of sample size and the analysis to be undertaken once the
test has been conducted and rely on the specification of somewhat artificial
acceptable and rejectable reliability levels. In this paper we offer an
alternative approach to sample size determination based on the idea of
assurance. This approach chooses the sample size to answer provide a certain
probability that the RDT will result in a successful outcome. It separates the
design and analysis of the RDT, allowing different priors for each. We develop
the assurance approach for sample size calculations in RDTs for binomial and
Weibull likelihoods and propose appropriate prior distributions for the design
and analysis of the test. In each case, we illustrate the approach with an
example based on real data.
