Reliability and optimal sensor design are of great interest for control engineers and the researcher community. The severity of faults is addressed through redundancy analysis. A structural analysis is introduced which uses symbolic calculus to determine which redundancy exists in the system and provides the means to find the particular sensor defaults. The paper is organized as follows. The first part gives an overview on Groebner bases and their programming. Definitions are included to specify explicitly what should be understood by the terms "symbolic calculus software" and more specifically lexicographic programming and Groebner base algorithms. The second part develops the concept of observability bases and in the third part we show how to use these bases to make optimal and reliable design. The biggest benefit of this method is the ability to extend the mathematical process to the n-linear case. (c) 2007 Elsevier Ltd. All rights reserved.