Accelerated repeated measures degradation tests can sometimes be used to assess product or component reliability when one would expect few or even no failures during a study. Such tests can be used to estimate the lifetime distributions of highly reliable items. This paper describes methods for selecting a single-variable accelerated repeated measures degradation test plan when the (possibly transformed) degradation is linear in (possibly transformed) time and unit-to-unit variability is described by a random effect. To find optimum test plans, we use a criterion based on a large-sample approximation to the estimation precision of the quantile of the failure-time distribution at use conditions. We also discuss how to find compromise test plans that satisfy practical constraints. We use the general equivalence theorem to verify that a test plan is globally optimum. The resulting optimized plans are also evaluated using simulation and compared with other test plans.