Sufficiency Condition for Stability of a Fully Coupled Design Process
Both in the deterministic and random DSM cases, the dynamics of a coupled design process is captured by a linear difference equation. Namely, the workload of a design task in the current design iteration is the sum of the redesign workloads caused by all the tasks it depends on. Unfortunately, the linear approximation is not so realistic, because it might lead to such a situation that the redesign workload of a task in later design iteration is more than the workload of its original design. As we know, this is impossible. Therefore, in this paper, we construct a new nonlinear dynamic equation for a concurrent fully coupled design process, in which the redesign workload of every design task in later iterations is not more than the workload of its original design. Then we find a sufficiency condition for the asymptotic stability of this coupled design process, and a method of estimating the iteration times that are needed for the workloads of this coupled design process to reduce to an acceptable level. Here, asymptotic stability means that design workload goes to zero when time goes to infinity; fully coupled means that every design task affects and depends on all the other tasks directly or indirectly.