In recent years, Approximate Computing Circuits (ACCs) have been widely used in applications with intrinsic tolerance to errors. With the increased availability of approximate computing circuit approaches, reliability analysis methods for assessing their fault vulnerability have become highly necessary. In this study, two accurate reliability evaluation methods for approximate computing circuits are proposed. The reliability of approximate computing circuits is calculated on the basis of the iterative Probabilistic Transfer Matrix (PTM) model. During the calculation, the correlation coefficients are derived and combined to deal with the correlation problem caused by fanout reconvergence. The accuracy and scalability of the two methods are verified using three sets of approximate computing circuit instances and more circuits in EvoApprox8b, which is an approximate computing circuit open source library. Experimental results show that relative to the Monte Carlo simulation, the two methods achieve average error rates of 0.46% and 1.29% and time overheads of 0.002% and 0.1%. Different from the existing approaches to reliability estimation for approximate computing circuits based on the original PTM model, the proposed methods reduce the space overheads by nearly 50% and achieve time overheads of 1.78% and 2.19%.