In this study, data on water shortage events were collected from customer service systems. An analysis was conducted to establish the relationship between customers’ complaints and the water pressure flow conditions. A mathematical model was developed to estimate the probability of water shortage events based on water head. The Sigmoid function is commonly used as an activation function in neural networks. The function of the model is the same as the Sigmoid function, and its critical parameters correspond to the service head requirements of water facilities. By considering the interaction between human emotions and artificial systems, this study provides novel insights into improving the operational control and construction of water distribution systems.