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This study aims to develop methods for detection of drift in sensor measurements. The study consists of three major components; 1) residual generation, 2) statistical change detection, and 3) model building. To identify the statistical properties of the residuals and to utilize them for detection of the drift, a new method for estimation of the drift rate is proposed. The method formulates an augmented system matrix model and processes the model using a Kalman filter. An analytical method for estimation of the drift rate is also derived. A Hamiltonian approach is used for evaluation of the steady state covariance of the residuals. The steady state covariance and the estimated drift rate enable the existence of the drift in the measurements to be determined in a statistical way using the change detection algorithms. The statistical change detection algorithms process the residuals to determine the drift statistically. In the study, performance of the major algorithms, including the Exponentially Weighted Moving average (EWMA), Cumulative Sum (CUSUM) control chart, and Generalized Likelihood Ratio Test (GRLT), are investigated. A new method for detection of the change, named the "Standardized Sum of the Innovation Test (SSIT)," is also proposed. The statistical properties of the decision function of the SSIT are derived to set the decision threshold statistically. A method for estimation of the mean delay of the SSIT is also derived. The mean delay of the SSIT is shown in a demonstration and is the shortest of the change detection algorithms. For demonstration purposes, mathematical models of a pressurizer in a CANada Deuterium Uranium (CANDU) nuclear power plant are developed. The mathematical models in the form of nonlinear differential equations are verified by comparing the simulation results with those of the industry standard code known as "CATHENA" (Canadian Algorithm for Thermal Hydraulic Network Analysis). The developed algorithms have been successfully applied to the pressurizer model for detection and estimation of pressure sensor drifts. The results convincingly demonstrate the effectiveness of the proposed algorithms in the detection of the drift.