Wu (2015) proposed the general weighted moments estimators (GWMEs) of the scale parameter of the one-parameter exponential distribution based on a multiply type II censored sample and claimed that the proposed estimator outperforms the other 14 estimators in terms of the exact mean squared errors (MSEs) in most cases. We (2015) used the GWMEs to construct the pivotal quantities to construct the prediction intervals for future observations. In practice, users also want to know the waiting times between two consecutive future observations. Therefore, in this paper we propose the prediction interval for future waiting times or interarrival time. One real life example is given to illustrate the prediction intervals based on GWMEs.