Parametric and Nonparametric Approaches to Optimal Design in Degradation Experiments with Saddlepoint Approximations

With advancements in technology, highly reliable products such as Li-ion batteries, transistors, and LEDs operate for extended periods without failure, making lifetime estimation challenging. Since these products degrade over time, degradation data modeled with stochastic processes can determine their failure time distribution. Given the long duration of degradation experiments, efficient experimental designs are crucial for optimizing sample size, measurement frequency, and total experiment time. This study proposes a generalized parametric saddlepoint approximation method for optimal design plans in degradation studies. Additionally, a robust nonparametric saddlepoint approximation procedure is introduced for cases where the underlying degradation process is unknown. Both methods develop optimal designs for the 100p-th percentile of the failure time distribution. Monte Carlo simulations and real-world degradation data applications validate the proposed methods, demonstrating their effectiveness compared to existing parametric and nonparametric approaches.