In this paper, we propose a delay dynamic coupled fault diagnosis (DDCFD) model to deal with the problem of coupled fault diagnosis with fault propagation/transmission delays and observation delays with imperfect test outcomes. The problem is to determine the most likely set of faults and their time evolution that best explains the observed test outcomes over time. It is formulated as a combinatorial optimization problem, which is known to be NP-hard. Since the faults are coupled, the problem does not have a decomposable structure as, for example, in dynamic multiple fault diagnosis, where the coupled faults and delays are not taken into account. Consequently, we propose a partial-sampling method based on annealed maximum a posteriori (MAP) algorithm, a method that combines Markov chain Monte Carlo and simulated annealing, to deal with the coupled-state problem. By reducing the number of samples and by avoiding redundant computations, the computation time of our method is substantially smaller than the regular annealed MAP method with no noticeable impact on diagnostic accuracy. Besides the partial-sampling method, we also propose an algorithm based on block coordinate ascent and the Viterbi algorithm (BCV) to solve the DDCFD problem. It can be considered as an extension of the method used to solve the dynamic coupled fault diagnosis (DCFD) problem. The model and algorithms presented in this paper are tested on a number of simulated systems. The results show that the BCV algorithm has better accuracy but results in large computation time. It is only feasible for problems with small delays. The partial-sampling algorithm has a smaller computation time with an acceptable diagnostic accuracy. It can be used on systems with large delays and complex topological structure.