Linear-spline approximation for semi-parametric modeling of failure data with proportional hazards

Modeling of failure processes using proportional hazards involves estimating both a baseline failure intensity as well as the parameters of the proportional failure intensity. In the absence of any information regarding the baseline failure intensity, a nonparametric form is typically assumed. This paper proposes a linear-spline function to approximate this baseline failure intensity, and develops such a spline function appropriate to bad-as-old failure data generated from a repairable system. Field data from an industrial setting demonstrate an improved approximation using such a spline function as compared to other procedures in the literature.