A new method for nonintrusive elevator fault detection is presented. A computationally efficient algorithm for implementing the method is also proposed. The method is employed to detect when the elevator has been stationary for an unusually long period of time compared to historical traffic load patterns. This information can be used for fault detection but also indirectly to monitor the condition of the doors. The traffic load on the elevator is modeled as a nonhomogeneous Poisson process, and a generalized linear model is used to describe how the intensity of the process varies over time. A statistical hypothesis test is then used to determine if the elevator has been stationary for an unusually long time. The application of the proposed method is illustrated by an example where the detected faults are compared with the elevator service log. All faults were detected long before the service company was notified by the facility owner. Furthermore, based on the evaluation of 30 weeks of data, the method achieves a precision of 0.82 at a recall probability of 0.80.