OBJECTIVES Meta-analysis is often conducted in OpenBUGS. This software, like all BUGS projects, is based on MCMC simulations by using Gibbs sampling. One of the main issues in the use of Markov chains in a continuous space is the chain convergence. If the chain does not converge, transient states will be accounted for in our posterior distributions. Since these states are not bound to the empirical data but only with the chain’s starting point, the estimated parameters of the posterior distribution will be biased. To help assessing the convergence of MCMC chain, several methods exist. METHODS Based on the literature, we run several simulation scenarios in order to test built-in OpenBUGS graphical methods and to assess the power of the “thin” approach, a fixed-step jumping-data method, for convergence. Then, we focus on the existing diagnoses, their supplementary assumptions and their associated computation costs. To help perform these diagnoses directly on BUGS objects, we present the R-package coda.   RESULTS The use of jumping-data method leads to loss of power and a poorer estimation of posterior distribution even in case of high autocorrelation. Consequently, the use of the thin method is not recommended to obtain a quicker convergence and better posterior distribution estimation. We have also seen that although autocorrelogram and trace can be useful to assess convergence, they can lead to misinterpretation in case of extremely low number of studies and conclude to convergence. Alternatively, using the Geweke diagnosis seems, in terms of computation cost and assumptions, recommended for two main advantages: it gives a measure of trust of being in a stationary process and very low computation cost. CONCLUSIONS We presented methods to assess convergence of MCMC chains and argued on their pros and cons. The Geweke diagnose was found to provide best trade-off between computational cost and interpretability.