  Accelerated degradation testing (ADT) is an effective way to evaluate the
lifetime and reliability of highly reliable products. Markovian stochastic
processes are usually applied to describe the degradation process. However, the
degradation processes of some products are non-Markovian due to the interaction
with environments. Besides, owing to the differences in materials and
manufacturing processes, products from the same population exhibit diverse
degradation paths. Motivated by this issue, an ADT model with memory effects
and unit-to-unit variability (UtUV) is proposed in this article. The memory
effect in the degradation process is captured by the fractional Brownian motion
(FBM) and the UtUV is considered in the acceleration model. Then, the lifetime
and reliability under the normal operating condition are presented. To give an
accurate estimation of the memory effect, a statistical inference method is
devised based on the expectation maximization (EM) algorithm. The effectiveness
of the proposed method is verified by a simulation case and a microwave case.
It is shown that the estimation of the memory effect obtained by the EM
algorithm is much more accurate than the traditional method. Moreover, without
considering UtUV in the ADT model, the estimation of the memory effect can be
highly biased. The proposed ADT model is superior in both deterministic
degradation trend predictions and degradation boundary quantification compared
to existing models.
