  In recent years, more attention has been paid prominently to accelerated
degradation testing in order to characterize accurate estimation of reliability
properties for systems that are designed to work properly for years of even
decades. %In this regard, degradation data from particular testing levels of
the stress variable(s) are extrapolated with an appropriate statistical model
to obtain estimates of lifetime quantiles at normal use levels. In this paper
we propose optimal experimental designs for repeated measures accelerated
degradation tests with competing failure modes that correspond to multiple
response components. The observation time points are assumed to be fixed and
known in advance. The marginal degradation paths are expressed using linear
mixed effects models. The optimal design is obtained by minimizing the
asymptotic variance of the estimator of some quantile of the failure time
distribution at the normal use conditions. Numerical examples are introduced to
ensure the robustness of the proposed optimal designs and compare their
efficiency with standard experimental designs.
