This paper presents an economic reliability-aware model predictive control (MPC) for the management of drinking water transport networks (DWNs). The proposed controller includes a new goal to increase the system and components reliability based on a finite horizon stochastic optimization problem with joint probabilistic (chance) constraints. The proposed approach is based on a single-layer economic optimization problem with dynamic constraints. The inclusion of components and system reliability in the MPC model using an Linear Parameter Varying (LPV) modeling approach aims to maximize the availability of the system by estimating system reliability. On the other hand, the use of a LPV-MPC control approach allows the controller to consider nonlinearities in the model in a linear like way. Moreover, the resulting MPC optimization problem can be formulated as a Quadratic Programming (QP) problem at each sampling time reducing the computational burden/time compared to solving a nonlinear programming problem. The use of chance-constraint programming allows the computation of an optimal strategy with a pre-established risk acceptability levels to cope with the uncertainty of the demand forecast. Finally, the proposed approach is applied to a part of the water transport network of Barcelona for demonstrating its performance. The obtained results show that the system reliability of the DWN is maximized compared with the other approaches.