Reliability modeling for two-phase degradation products based on the inverse Gaussian process

Reliability analysis based on degradation data is of great significance for highly reliable units. For some units, their degradation rates may change at a certain time due to some internal or external reasons, which makes the degradation paths exhibit a two-phase degradation pattern. In this paper, a two-phase inverse Gaussian degradation process model is proposed to fit the degradation data with two-phase pattern. Two different nonlinear inverse Gaussian processes are separately used to model the two stages of the degradation path. The parameter estimation of the model is divided into three steps. Firstly, the Schwarz information criterion is applied to determine the time interval in which the change point is located based on each degradation path. Subsequently, the change point is estimated using the generalized least square method. Next, the distribution of the change point of the two-phase degradation model is estimated. Finally, the model parameters are estimated by employing the maximum likelihood method. The expressions of the reliability function and the distribution function of the remaining useful lifetime of the system are derived explicitly. Numerical simulations are conducted to illustrate the two-phase degradation model, and the liquid coupling device data is utilized to validate the proposed methodologies.