## 3 Task-Based Dynamic Disassembly Process Model
For each disassembly operation (normal node) on the operation layer, there is a task graph corresponding to it on the task layer. The task graph contains all possible task sequences for completing the operation. Note that a task sequence consists of multiple elementary tasks that jointly complete an operation. Unlike a disassembly operation, which is always feasible, whether a task in a task sequence is feasible depends on the current state of the component or subassembly to be disassembled. For example, if the component to be disassembled is detected as damaged, tasks used in the normal state of the component are not feasible, and they cannot be chosen to complete the corresponding operation. The state of a component needs to be identified by sensor feedback. In addition, some task processing times in TD-TAOG are time-varying due to the influence of uncertain human abilities and behaviours. Clearly, the introduction of the task graph for each operation gives the possibility of processing various dynamic operations intuitively and practically, considering the uncertainty of the disassembly process. TD-TAOG contains three types of nodes, artificial nodes, normal nodes, and unit nodes, with two types of hyperarcs: AND-type hyperarcs and OR-type hyperarcs. Among them, the definitions of artificial nodes, normal nodes, AND-type hyperarcs, and OR-type hyperarcs are the same as the corresponding definitions in the TAOG. Unit nodes in the task layer represent elementary tasks, including disassembly and supplementary tasks. To distinguish these two types of hyperarcs, we use a slight curve as the mark of the OR-type hyperarcs. A flashlight [45] is taken as an example of a product to better illustrate TD-TAOG. The flashlight is constructed with seven components and their connections, as shown in Figure 1. Figure 1 contains the cross-section view and the connection diagram of the flashlight. The TD-TAOG of the flashlight in the \(\ell\)th environment is given in Figure 2. In Figure 2, subassemblies, disassembly operations, and tasks are modelled by artificial nodes labelled \(A_{a}\)s, normal nodes labelled \(B_{b}\)s, and unit nodes labelled \(U_{u}\)s. The number sequence next to each artificial node represents the related subassembly. For instance, artificial node \(A_{6}\) represents the subassembly '5/7', which consists of component five (main housing), component six (spring), and component seven (battery). For simplicity, in Figure 2, subassemblies with only one component are not shown. Furthermore, only the task graph of operation \(B_{9}\) is shown in Figure 2. The operation layer has four AND-type hyperarcs and two OR-type hyperarcs. In addition, Figure 2 provides numerous possible disassembly sequences, such as the disassembly sequence [\(B_{1}\), \(B_{8}\), \(B_{4}\), \(B_{7}\), \(B_{9}\), and \(B_{10}\)]. Based on feedback from the sensors, the state of an artificial node or a normal node can be determined in real time. In the example shown in Figure 2, since component three (bulb) is detected as being lost at the starting time instant of the \(\ell\)th environment, nodes \(A_{1}\), \(A_{4}\), \(B_{3}\), and \(B_{7}\) are determined to be in the missing state. Component four (head housing) is detected as damaged; therefore, nodes \(A_{3}\), \(B_{4}\), and \(B_{6}\) are determined to be in the damaged state. In the task graph of operation \(B_{9}\), \(U_{ini}\)\({}^{9}\) and \(U_{ter}\)\({}^{9}\) are the initial and terminal nodes, respectively. These two dummy nodes (dummy tasks) are introduced to obtain feasible task sequences. Each directed arc in the task graph represents  
Figure 1: An example of a product: (**a**) a flashlight [45] and (**b**) the connection diagram of the flashlight. Figure 2: The TD-TAOG of the flashlight in the \(\ell\)th environment. an ordered task pair. We need to find a path consisting of feasible unit nodes (tasks) from \(U_{ini}\)9 and \(U_{ter}\)9 as a feasible task sequence to complete \(B_{9}\).