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This paper proposes a new model, called the 2-parameter Engelhardt-Bain process (2-EBP) model, to describe the failure pattern of complex repairable systems subjected to reliability deterioration with the operating time, and showing a finite bound for the intensity function. The characteristics of the 2-EBP model are discussed, and the physical meaning of its parameters is derived. The 2-EBP model can be viewed as a dynamic power law process, whose shape parameter ranges from 2 to 1 as the system age increases, converging asymptotically to the homogeneous Poisson process. Maximum likelihood estimates of model parameters & other quantities of interest, as well as a testing procedure (based on the likelihood ratio statistic) for time trend, are provided. Numerical applications are given to illustrate the 2-EBP model & the related inferential procedures, and to emphasize on the caution to use in assuming the (very often used) power law process when the presence of a finite bound for the failure intensity is conjecturable.