Abstract Human computation systems harness the cognitive power of a crowd of humans to solve computational tasks for which there are so far no satisfactory fully automated solutions. To obtain quality in the results, the system usually puts into practice a task replication strategy, i.e. the same task is executed multiple times by different humans. In this study we investigate how to improve task replication considering information about the credibility score of participants. We focus on how to automatically measure the credibility of participants while they execute tasks in the system, and how such credibility assessment can be used to define, at execution time, the suitable degree of replication for each task. Based on a conceptual framework, we propose (i) four alternative metrics to measure the credibility of participants according to the degree of agreement among them; and (ii) an adaptive credibility-based task replication algorithm that defines, at execution time, the degree of replication for each task. We evaluate the proposed algorithm in a diversity of configurations using data of thousands of tasks and hundreds of participants collected from two real human computation projects. Results show that the algorithm is effective in optimising the degree of replication, without compromising the accuracy of the obtained answers. In doing so, it improves the ability of the system to properly use the cognitive power provided by participants.