Accelerated degradation data analysis based on inverse Gaussian process with unit heterogeneity

The unit heterogeneity of products and the nonlinear parameter-stress relationship often exist in practice. Therefore, considering the unit heterogeneity, the nonlinear accelerated model and inverse Gaussian process are developed to depict the accelerated degradation data. On the other hand, this more realistic model leads a challenge to derive the model parameter interval estimation. Thereby, a novel two-step interval estimation method is proposed for the proposed accelerated degradation model. First, generalized confidence intervals of the parameters characterizing random effect are derived from the Cornish-Fisher expansion, and their cumulative distribution functions are obtained. Then, using the generalized pivotal quantity procedure, generalized confidence intervals of the accelerated model parameters are derived. In addition, generalized confidence intervals of predictive reliability indexes are derived to guide the practical application. Finally, simulation studies and two real examples on Spiral springs and integrated circuit devices are presented to demonstrate the implementation of the proposed method.

Automated summary

This paper develops a nonlinear accelerated model and inverse Gaussian process for depicting accelerated degradation data, considering the unit heterogeneity and nonlinear parameter-stress relationship. To address the challenge of parameter interval estimation, a novel two-step interval estimation method is proposed. The method derives generalized confidence intervals of random effect parameters and accelerated model parameters, as well as predictive reliability indexes, using the Cornish-Fisher expansion and generalized pivotal quantity procedure. Simulation studies and real examples demonstrate the effectiveness of the proposed method.