Conducting preventive maintenance of measurement sensors in real-time during process operation under feedback control while ensuring the reliability and improving the economic performance of a process is a central problem of the research area focusing on closed-loop preventive maintenance of sensors and actuators. To address this problem, a robust moving horizon estimation (RMHE) scheme and an economic model predictive control system are combined to simultaneously achieve preventive sensor maintenance and optimal process economic performance with closed-loop stability. Specifically, given a preventive sensor maintenance schedule, a RMHE scheme is developed that accommodates varying numbers of sensors to continuously supply accurate state estimates to a Lyapunov-based economic model predictive control (LEMPC) system. Closed-loop stability for this control approach can be proven under fairly general observability and stabilizability assumptions to be made precise in the manuscript. Subsequently, a chemical process example incorporating this RMHE-based LEMPC scheme demonstrates its ability to maintain process stability and achieve optimal process economic performance as scheduled preventive maintenance is performed on the sensors. (c) 2015 American Institute of Chemical Engineers AIChE J, 61: 3374-3389, 2015