The rapid developments in the sensor and its related technology have made automation possible in many processes in diverse fields. Also sensor-based fault diagnosis and quality improvements have been made possible. These tasks depend highly on the sensor network for the accurate measurements. The two major problems that affect the reliability of the sensor system/network are sensor failures and sensor anomalies. The usage of redundant sensors offers some tolerance against these two problems. Hence the redundancy analysis of the sensor system is essential in order to clearly know the robustness of the system against these two problems. The degree of sensor redundancy defined in this thesis is closely tied with the fault-tolerance of the sensor network and can be viewed as a parameter related to the effectiveness of the sensor system design. In this thesis, an efficient algorithm to determine the degree of sensor redundancy for linear sensor systems is developed. First the redundancy structure is linked with the matroid structure, developed from the design matrix, using the matroid theory. The matroid problem equivalent to the degree of sensor redundancy is developed and the mathematical formulation for it is established. The solution is obtained by solving a series of l1-norm minimization problems. For many problems tested, the proposed algorithm is more efficient than other known alternatives such as basic exhaustive search and bound and decomposition method. The proposed algorithm is tested on problem instances from the literature and wide range of simulated problems. The results show that the algorithm determines the degree of redundancy more accurately when the design matrix is dense than when it is sparse. The algorithm provided accurate results for most problems in relatively short computation times.