Abstract: The equation such asf=C_1+C_2 \int_0^t\left\exp \int_0^u \omega(s) \mathrmd s\right \mathrmd u, where C₁,C₂ are arbitrary constants and w（s） is Lebesgue square integrable, is the famility of monotone function. In particular the function w（s） is supposed to be a spline function in this paper. The parameters are estimated by the penalized least square method and the asymptotic of the estimator is obtained. Application is discussed to the analysis of the degradation data and the satisfying result is made.