Offshore platforms are prone to fatigue damage. To evaluate the fatigue damage, these platforms are periodically inspected during the in-service lifetime. Inspection activities provide additional information, which includes detection and measurement of crack size. A Bayesian framework can be used to update the probability distribution of the uncertain parameters such as crack size. After updating the distribution of the crack size, it is possible to improve the estimation of joint reliability. The main purpose of this study is to present different methods of Bayesian inference to update the probability distribution of the crack size using the inspection results and to demonstrate how the results are different. Two different methods are presented: analytical (conjugate) and numerical methods. The advantages and shortcomings of each method are discussed. To compare the results of the analytical and numerical methods, two different situations are considered; updating the crack size distribution for a particular joint and updating the crack size distribution for several joints that have almost the same conditions. Although the proposed methodology can be applied to different kinds of structures, an example of tubular joints in a specific jacket platform is presented to demonstrate the proposed approach and to compare the results of two methods.