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When the residual of model did not agree with normal distribution or included abnormal data because of the intensive disturbed noise, the Lipschitz exponents calculated with the least square method would generate obvious deviation. In order to improve the robustness and the efficiency of the algorithm of the Lipschitz exponents of the wavelet singularity analysis, the weight function based on the least median of squares (LMS) was constructed. Further, the improved algorithm with the weighted least square method was put forward. The diagnosis results show that with the improved weighted least square method based on LMS, the Lipschitz exponents can be calculated exactly to determine the criterion avoiding the influence of the abnormal data in signals. So, the valve spring abruption fault of emulsion pump can be identified correctly and accurately. At the same time the singularities in the signals can be localized to find the impact hour of valve disc to realize the qualitative analysis of the volumetric efficiency of emulsion pump.