Gaussian Process (GP) models are increasingly finding application in wind turbine condition monitoring and in particular early fault detection. GP model accuracy is greatly influenced by the choice and type of the covariance functions (used to described the similarity between two given data points). Hence, the appropriate selection and composition of covariance functions is essential for accurate GP modelling. In this study, an in-depth analysis of commonly used stationary covariance functions is presented in which wind turbine power curve used where GP based power curve has been constructed using different stationary covariance functions, and after that, a comparative analysis has been carried out in order to identify the most effective covariance function. The commonly used squared exponential covariance function is taken as the benchmark, against which other covariance functions are assessed. The results show that the performance (in terms of model accuracy and uncertainty) of GP fitted power curve models based on rational quadratic covariance functions is almost the same as for the most commonly used squared exponential function. Thus, rational quadratic covariance functions can be used instead of squared exponential covariance functions. In this paper, strength and weakness of stationary covariance functions would be highlighted for effective condition monitoring. Crown Copyright (C) 2019 Published by Elsevier Ltd. All rights reserved.