Analytical approach for designing accelerated degradation tests under an exponential dispersion model

To provide timely lifetime information of manufactured products to potential customers, designing an efficient accelerated degradation test (ADT) is an important task for reliability analysts. In the literature, several papers have addressed a general k-level ADT design problem (including the determinations of the number of stress levels (k), testing stresses, allocation of test units and termination times) when the underlying degradation path follows an exponential dispersion model. The results are practical and interesting. However, most of those studies only addressed the case of k≤4. Generally, if a direct proof (such as using the Karush–Kuhn–Tucker conditions) for the case of k>4 is intractable, we can consider an indirect proof via the general equivalence theorem. In this paper, we first propose a conjecture optimal design for a k-level ADT design problem and then apply the general equivalence theorem to show that this conjecture design turns out to be the global V-optimal design. In addition, an example is used to illustrate the proposed procedure. The main contribution of this work is that this analytical approach can provide reliability analysts with better insight for designing an efficient ADT plan.