The simple calculated permutation entropy is an intuitive index to measure the complexity of a time series by a comparison of neighbouring values, therefore, it can be used to detect dynamical changes in a time series. However, in permutation entropy, the amplitude information of a time series is ignored. By incorporating the variance information, weighted permutation entropy (WPE) can derive stable results, and enable the detection of abrupt changes in a time series. In this paper, weighted permutation entropy is employed to build the performance index from the closed loop output time series to monitor the control loop performance. Furthermore, two control charts are established to define the control limits for sample estimations of the WPE-based performance index. In this study, the Shewhart control chart and the exponentially weighted moving average (EWMA) control chart are integrated to develop two control performance monitoring schemes, Shewhart-WPE and EWMA-WPE. In addition, a numerical simulation is used to illustrate the ability and effectiveness of the developed Shewhart-WPE scheme. The proposed EWMA-WPE scheme is applied to monitor a natural gas pipeline transportation pressure control loop. The effectiveness of the proposed Shewhart-WPE and EWMA-WPE schemes is verified by the results.