Abstract
Accelerated tests are widely used to assess the lifetime information for highly reliable products. Due to different types of collected data, the accelerated tests can be further classified as accelerated life tests (ALTs) and accelerated degradation tests (ADTs). For highly reliable products, conducting an accelerated test is very costly. To obtain the precise prediction of lifetime information, how to design an efficient planning under cost constraints is a critical task. For the planning of accelerated tests, this study includes the following three topics: (i) Several researchers have attempted to address the problem of determining the sample size allocation and the settings of stress levels, but their results have been based only on specific degradation models. Therefore, they lack a unified approach toward general degradation models. We first proposes a class of exponential dispersion (ED) degradation models which include some special cases such as the Wiener, gamma, and inverse Gaussian processes. Assuming that the underlying degradation path comes from the ED class, we analytically derive the optimum allocation rules by minimizing the asymptotic variance of the estimated q quantile of product’s lifetime for two-level and three-level ADT allocation problems no matter the testing stress levels are prefixed. (ii) Assuming that the underlying degradation path comes from the ED class, we further determine the total sample size, the number of measurements within a degradation path, and the total testing times simultaneously under the constraints of total experimental cost. For this constrained optimization, we propose an algorithm to determine the optimum design by minimizing the asymptotic variance of the q quantile of the product’s lifetime. (iii) There has been a lot of development in optimum test planning, most of the methods assume that the true parameter values are known. However, in reality, the true model parameters may depart from the planning values. Therefore, we use Bayesian framework and propose a sequential test planning strategy for ALTs. Furthermore, we apply the proposed strategy to the accelerated cyclic fatigue tests of polymer composite materials which are lightweight and comparable levels of strength and endurance. We also use extensive simulation to study the properties of the proposed sequential test planning strategy.