Fatigue-induced crack initiation and growth is a common phenomenon in a cyclically loaded structure. The crack due to fatigue reduces the structure's strength and increases the risk of its failure. Engineers have been using degradation models like Paris' law for crack length prediction to schedule repair and maintenance of such structures. Paris' law is a widely used physical degradation model that relates crack length to the magnitude of the applied load. Though, finding the proper value of Paris' law parameters is challenging due to many factors such as crack growth uncertainty. Several methods are available to quantify the crack growth uncertainty, and many of them treat Paris' law parameters as random variables that follow a distribution. Those methods used optimization to estimate the mean and standard deviation of the parameters’ distribution; however, the optimization strategy used in those methods may generate a large standard deviation. Moreover, the magnitude of the applied cyclic load is often known though there can be situations when it is unknown. Dealing with an unknown magnitude of applied load is not adequately investigated in existing methods, and some have even neglected the load value in Paris' law equation. This thesis studies the fatigue crack propagation in an aluminum alloy plate and proposes an optimization method that estimates the Paris' law parameters and their standard deviation. The optimization method also considers the case of the unavailable magnitude of the applied load. The optimized parameters are further updated using Bayesian updating with the help of condition monitoring data. Existing crack growth data for an aluminum alloy plate is used to develop and validate the proposed method. The validation results show that after the 96th update performed at 71% of maximum allowable crack length, the average error in the lifetime prediction is 1.5%.