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• In this paper, the nonlinear fault detection observer is constructed and the observer gain function is derivated by choosing the novel Lyapunov functions. The predetermined estimation accuracy-dependent nonnegative function is introducing in the last step of recursive algorithm. • The threshold design problem is solved by suppressing the residual within the predetermined output estimation accuracy range during the implementation process of observer. • The tight thresholds ϵ and ϵ are predetermined under strategic designing scheme. It is straightforward to implement by comparison with the existing empirical or calculation methods of threshold. This paper presents an fault detection (FD) method for a class of uncertain nonlinear systems with unmatched nonlinear fault functions and disturbances. A recursive FD observer is designed with predetermined and small output estimation error. The nonlinear observer gain function is achieved by introducing predetermined output estimation accuracy-dependent nonnegative functions. Combining Lyapunov functions, it is shown that the absolute value of the residual signal is equal or lesser than tight threshold before fault occurrence. The FD scheme is proposed following fault detectability analysis, simulation example indicates the validity of the proposed method. [ABSTRACT FROM AUTHOR]