The aim of this study is to generalize the power Rayleigh distribution using the quadratic rank transmutation map to obtain the transmuted power Rayleigh distribution. Some important statistical and reliability properties of the transmuted power Rayleigh distribution such as hazard rate, moments, quantiles, order statistics and some sub-model distributions are obtained. The maximum likelihood method based on Type II censoring is applied to estimate the unknown parameters, reliability and hazard rate functions of the transmuted power Rayleigh distribution. In addition, a simulation study is performed to illustrate the theoretical results and the precision of the maximum likelihood estimates. Finally, two applications are applied to demonstrate the importance and flexibility of the new model.