Computers and Chemical Engineering 23 (2000) 1757 – 1762 Cost-optimal design of reliable sensor networks Miguel Bagajewicz a, *, Mabel Sa ´nchez b a School of Chemical Engineering and Materials Science, Uniersity of Oklahoma, 100 E. Boyd Room, T-335, Norman, OK 73019, USA b Planta Piloto de Ingenierı ´a Quı ´mica (UNS – CONICET), C.C. 717, Camino La Carrindanga Km 7, (8000) Bahı ´a Blanca, Argentina Received 7 December 1998; received in revised form 29 November 1999; accepted 29 November 1999 Abstract Several papers have been presented in the last years regarding the design of reliable sensor networks. In all these papers, the system reliability was maximized, constrained by a fixed number of sensors. In these models, the cost has played an indirect unclear role. A minimum cost model for the design of reliable sensor networks is presented in this paper. The connections with previous models are established, showing that they are a particular case of the model stated in this work. © 2000 Elsevier Science Ltd. All rights reserved. Keywords: Sensor network design; Reliability; Data reconciliation; Instrumentation cost www.elsevier.com/locate/compchemeng 1. Introduction Sensors are needed in a process plant for a variety of purposes. The most important are control and monitor- ing, but other non-traditional activities such as safety, fault detection and production accounting have been incorporated as clients of a data processing system. Recently, on-line optimization has added new needs for reliable process data of good quality. Consequently, the selection of sensors in chemical plants to fulfill reliabil- ity issues has emerged as a topic of interest. Ali and Narasimhan (1993) proposed to maximize reliability, which is based on sensor failure probability, observability of variables as well as redundancy. They introduced the concept of reliability of estimation of a variable. In addition they proposed to measure the reliability of the system as the smallest reliability among all variables. While looking at all networks containing the minimum set of sensors to achieve observability they formulated a Max – Min problem using reliability as the objective function. Lately, Ali and Narasimhan (1995) extended their previous work to redundant net- works. Their algorithm uses graph theory to build networks with a specified number of sensors and maxi- mum system reliability. In a recent paper, Sen, Narasimhan and Deb (1998) presented a genetic al- gorithm that can be applied to design non-redundant sensor networks using different objectives functions. Departing from graph theory and linear algebra ap- proaches, Bagajewicz (1997) formulated a MINLP problem to obtain cost-optimal network structures for linear systems subject to constraints on precision and robustness, that is defined in terms of measures that allow the sensor network to effectively manage gross errors. This paper concentrates on the connection between the models based on reliability goals and the minimum cost model subject to reliability constraints. The mini- mum-cost model subject to reliability constraints is presented first. Following, the Maximum Reliability Model presented by Ali and Narasimhan (1993, 1995) is reviewed and its connections to mathematical program- ming are analyzed. In the next section, a Generalized Maximum Reliability model is presented, that is derived using the minimum cost model as starting point and a duality property of optimization problems. The connections to the model developed by Ali and Narasimhan (1993) are established next. Finally, exam- ples are shown illustrating the power of the minimum cost approach in terms of its ability to handle situations and constraints that the maximum reliability model cannot solve. * Corresponding author. Tel.: +1-405-3255811; fax: +1-405- 3255813. E-mail addresses: bagajewicz@ou.edu (M. Bagajewicz), msanchez@plapiqui.edu.ar (M. Sa ´nchez) 0098-1354/00/$ - see front matter © 2000 Elsevier Science Ltd. All rights reserved. PII:S0098-1354(99)00324-5