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In this paper, a fault diagnosis scheme for a class of time-varying faults using output probability density estimation is presented. The system studied is a nonlinear system with time delays. The measured output is viewed as a stochastic process and its probability density function (PDF) is modeled, which leads to a deterministic dynamical model including nonlinearities, uncertainties. The fault considered in this paper is time-varying, piecewise continuous with finite discontinuous points. A new adaptive fault diagnosis algorithm is proposed. An ideal estimation of the fault and its modified form are analyzed. Simulation example is given to demonstrate the effectiveness of the proposed approaches.