Today, more and more home appliances are equipped with networking capabilities as a part of the Internet of Things (IoT) and can be controlled remotely on a phone or computer to build smart homes. Nevertheless, to date, the majority of IoT devices in smart homes still necessitate human intervention for operation and the smart homes lack sufficient intelligence. Autonomous management can maximise the benefits of IoT technology to create a more intelligent smart home environment. Semi-Markov models, a Process Mining technique capable of providing the probabilistic framework, is used in this paper to analyse the historical records of IoT systems, which essentially reflect users’ habitual activities of daily living (ADL). Through data analysis and reasonable assumptions, a weighted convolutional distribution is proposed to fit the time gaps between device activations. This model is used to predict IoT devices’ activation sequence and timing. With efficient predictions, devices can autonomously prepare, or turn on/off before users interact with them, thus providing a better living experience. The proposed method is validated on a public smart home dataset with hypothesis tests to evaluate the performance.