Kernelized Proportional Intensity Model for Repairable Systems Considering Piecewise Operating Conditions

The proportional intensity model (PIM) has been used to model the intensity function of repairable systems taking non-time factors, such as operating conditions, and repair history, into consideration. This paper develops a kernelized PIM (KPIM) by combining the PIM and the kernel method to consider a scenario where a repairable system experiences piecewise operating conditions. The kernel method is used to approximate the PIM covariate function nonlinearly. An approach based on the regularized likelihood function is proposed to obtain the optimal parameters for the KPIM. A numerical example is provided to demonstrate the KPIM model, and the parameter estimation approach.