Monitoring the activities of daily living (ADL) in smart homes is crucial, especially for older people and patients, to maintain or enhance their functioning, independence, and overall well-being. Additionally, by detecting unusual or abnormal inhabitant behaviour, it provides an opportunity for facilitating reminders, customised assistance for ADL completion, or alarms to notify carers or medical services. This study utilizes semi-Markov models integrated with gamma mixture models for modelling ADLs, as well as identifying anomalies, especially long holding times. The method is evaluated on a publicly available sensorised smart home dataset, with 2, 12 and 2 anomalies detected in activities, sensors and locations respectively, demonstrating its effectiveness in ADL modelling and anomaly detection.