Abstract: Acceleration is widely used in reliability tests to yield sufficient reliability information within a short time frame. From the statistical point of view, the cost of acceleration is that additional parameters are needed to link the accelerating variables to the failure process. When the increase of statistical information is insufficient to compensate the introduction of additional parameters, acceleration is inefficient. This scenario may be rare in a life test, as acceleration yields more failures and failure is more informative than censoring. In a degradation test, however, information contained in a degradation measurement under high stress levels may not be much higher than that under normal use conditions; in this connection, acceleration may not be always necessary. This study identifies situations where acceleration is unnecessary when some common stochastic process models are used, including the Wiener, gamma, and inverse Gaussian (IG) processes. We assume that both the degradation rate and the volatility of degradation process are functions of the accelerating variable. An acceleration relation index is introduced to unify different kinds of acceleration relations seen in the literature. It is shown that when the acceleration relation index is at least one, acceleration is always inefficient. Otherwise, the necessity of acceleration depends on values of the model parameters as well as the acceleration relation index. These results are unified using a class of stochastic process models called the exponential dispersion (ED) class. A numerical example is given to illustrate the procedure.

Key words and phrases: Accelerated degradation test, exponential dispersion models, reliability, stochastic process models.