The improved empirical fragility model addresses statistical dependence among observations of seismic performances, which arises from common but unknown factors influencing the observations. The proposed model accounts for this dependence by explicitly including common variables in the formulation of the limit state for individual components. Additionally, the fact that observations of the same component during successive earthquakes are correlated is considered in the estimation of the model parameters. As demonstrated by numerical examples considering the fragility of electrical substation equipment, the improved formulation can lead to significantly different fragility estimates than those obtained with the conventional assumption of statistical independence among the empirical observations. Furthermore, the conventional approach underestimates the statistical uncertainty associated with the resulting fragility estimates. The paper concludes with an investigation of the effects of statistical uncertainty and component statistical dependence on the system fragility. Numerical examples demonstrate that these effects are significant and must be addressed in the analysis of redundant systems.