Abstract

For highly reliable products, accelerated degradation tests (ADTs) are often used to obtain degradation and/or failure data to estimate the lifetime distribution in a timely manner for developing, for example, a product warranty policy or a process maintenance schedule. The step-stress ADT (SSADT) and parallel constant-stress ADT (PCSADT) are two commonly used ADTs. However, there is no study on whether these two types of ADT are indeed optimal ADTs within a wider class of ADTs with arbitrary stress functions. Furthermore, researchers also consider the experimental cost, either as the objective function or as a constraint, when developing an optimal test plan. As a result, certain lifetime estimates may not be sufficiently accurate or precise. In this paper, we first show that, for any design with an arbitrary stress function, there exists a corresponding statistically equivalent SSADT design with the same Fisher information matrix of parameter estimates and hence the same values for the four commonly-used optimality criteria considered in a reliability study. We also show that the SSADT and PCSADT are statistically equivalent under some mild conditions. This implies we can focus only on SSADT or PCSADT. Furthermore, we show that the optimal ADT is either a simple PCSADT or a simple SSADT using only the minimum and maximum stress levels. With these results, we then propose a two-stage procedure for developing optimal ADTs that takes the estimation accuracy as well as the experimental cost into account when estimating the Mean-Time-to-Failure (MTTF) and pth percentile (t_p) of the lifetime distribution. In the first stage, we obtain the (statistically) optimal simple ADT designs by controlling the margin of errors (precisions) of the lifetime estimates and, in the second stage, we determine the minimum experimental resources allocation and the optimal experiment termination time under a cost consideration. Explicit solutions are obtained. Finally, we use the light emitting diode (LED) testing as an example to illustrate our methods and compare with some existing results in the literature.