Diagnosing incipient short circuit (SC) of on-board lithium-ion cells is of great importance for safety operation, because it can prevent further deterioration such as spontaneous thermal runaway. Considering equivalent circuit models (ECMs) are currently the most used models for executing on-line battery state and parameter estimation, hence the purpose of this study is to propose a general battery incipient SC detection method through the commonly used ECMs. Model generality, design generality and implementation generality are the main design criteria. In this paper, inspired by the concept of Takagi-Sugeno fuzzy system, a weighting function self-regulating non-linear robust state and fault estimator that is designed for battery SC detection is proposed. Namely, the slowly changing characteristic of battery state of charge (SOC) is fully taken into account to construct a weighting function self-regulating mechanism among different design segments. Genetic algorithm has been used for the membership function tuning. Therefore, incipient SC detection is addressed from the perspective of fault estimation. The absolute estimation error of battery SOC after the SC fault occurrence is smaller than 0.01 regardless of the SC resistance values. Furthermore, considering the estimated fault signal is usually corrupted with noise in reality, a statistical technique, namely Cumulative Sum, is employed to detect the tiny change of the signal due to the incipient fault. Theoretical and methodological contributions are the main aims of this research work. Intensive numerical simulations with real experimental data have verified the effectiveness of the proposed incipient SC detection method.