Shewhart-type attribute charts are known to be inefficient for small changes in monitoring nonconformities. An alternative way is to use a time-weighted chart to monitor the time between events (TBE). We propose a one-sided Generally Weighted Moving Average control chart to monitor the time between events (TBE); regarded as the GWMA-TBE chart. To aid the implementation of the chart, the necessary design parameters are provided. An extensive performance analysis shows that the GWMA-TBE chart is better than the well-known EWMA and Shewhart charts at detecting very small to moderate changes. Finally, a summary and some conclusions are provided.