In real-life situations characteristics of Web service systems evolve in time. Therefore, change detection techniques become substantial elements of adaptive procedures for Web service systems management, such as resource allocation and anomaly detection methods. In this paper, we propose an on-line change detector which uses the Bayesian inference. We define two models which describe situations with one change and no change within data. Next we apply Bayesian model comparison for change detection. In order to obtain analytical expressions of model evidences used in the model comparison we provide a coherent framework of change detection which focuses on an approximation of the Bayes factor. The proposed solution, contrary to state-of-the-art methods, works in an on-line fashion and the algorithm's computational complexity is proportional to the constant size of the shifting window. Low computational complexity of the change detector enables its application in complex computer networks. At the end of the research paper, the quality of the proposed algorithm is examined using simulated Web service system.