Analyzing Accelerated Degradation Data via an Inverse Gaussian Degradation Model with Random Parameters

A degradation model with random parameters can improve the accuracy of reliability assessment compared with that with fixed parameters. However, it is difficult to apply the degradation model with random parameters to straightforwardly analyze accelerated degradation data. To overcome this problem, a method applying the random parameter Inverse Gaussian degradation model to analyze accelerated degradation data was studied in this paper. Acceleration factor constant principle was used to deduce the relationships that the parameters of Inverse Gaussian degradation model should satisfy under different stresses. Then, the expression of acceleration factor for an inverse Gaussian degradation model was obtained. The degradation data under accelerated stress levels was transformed to the equivalent degradation data under the normal stress level based on acceleration factors. The conjugate prior distributions of random parameters were applied and Expectation Maximization algorithm was designed to estimate hyper parameters. Simulation tests validated the feasibility and effectiveness of proposed method, and a case study demonstrated the proposed method has a good engineering application value.