A duality based framework for integrating reliability and precision for sensor network design

In sensor network design literature, requirements such as maximization of the network reliability [Y. Ali, S. Narasimhan, Sensor network design for maximizing reliability of linear processes, AIChE J. 39 (1993) 820–828; Y. Ali, S. Narasimhan, Redundant sensor network design for linear processes, AIChE J. 41 (1995) 2237–2249] and minimization of cost subject to precision constraints [M. Bagajewicz, Design and retrofit of sensor networks in process plants, AIChE J. 43 (1997) 2300–2306; M. Bagajewicz, E. Cabrera, New MILP formulation for instrumentation network design and upgrade, AIChE J. 48 (2002) 2271–2282] have been proposed as a criteria for optimally locating sensors. In this article, we show that the problems of maximizing reliability and maximizing precision (or minimizing variance) for linear processes are dual of each other. To achieve this duality, we propose transformations which can be used to convert sensor failure probabilities into equivalent sensor variances and vice versa. Thus, the duality enables working in a single framework with specified criteria on reliability as well as precision. As an application of this duality, we propose two formulations for the sensor network design problem viz., maximization of the network reliability subject to precision constraints and minimization of the network variance subject to reliability constraints. We also show the utility of these formulations to determine the pareto-front for the combinatorial sensor network design problem. Hydrodealkylation and steam-metering case studies are used to illustrate the proposed ideas.