Oscillation and hazard functions

In the medical data analysis, the shapes of hazard functions are very important for the survival analysis. The simple dimensional hazard function is given by r(t) = f(t)(1 − F(t)), 0 ≤ F(t) < 1, where f(t) is a probability density function with its distribution function F(t). In this paper, we discuss the hazard function, list the results of its mathematical parts as much as possible, and study the oscillatory properties of first- and second-order functional differential equations related to hazard functions.