Nonlinear Mixed-Effects Models for Multiple Repairable Systems

The multiple repairable systems may present system-to-system variability owing to the factors such as operation environments and working intensities of individual systems. It may be more reasonable to assume a heterogeneity among all the systems. In this paper, we propose a nonlinear mixed-effects model (NLMM), called power law process-nonlinear mixed-effects model (PLP-NLMM) and log linear process-nonlinear mixed-effects model (LLPNLMM), which model the failure patterns of a multiple repairable systems having monotonic trend. The purpose of this research is to provide flexible applications of mixed-effects models to the reliability analysis of multiple repairable systems, mainly based on the nonhomogeneous Poisson process (NHPP). The proposed models are applied to the failure data of the hydraulic system of load-haul-dump (LHD) machines. Finally, the results from the PLP-NLMM and LLP-NLMM are compared with those from PLP, LLP and PLP-GLMM in terms of parameter estimation and its precision.