Concurrent engineering design using interval methods

Modern design practice has displaced serial approaches in favour of concurrent engineering design, which takes several fields simultaneously into consideration, using interaction and iteration to proceed towards generally acceptable solutions. Concurrent design is very often based upon a mathematical model, which not only defines the properties and capabilities of a product, but also economic and production aspects, such as costs, tooling, machine loading and scheduling, and leads to some ‘optimum’ solution satisfying all requirements as closely as possible. This scenario does not reflect actual design activity. Each team member usually has a set of approximate requirements, which can be expressed as a range of admissible values of the design parameters. The aim is to resolve these demands, and determine a set of consistent parameter ranges which then define the design space. Iteration on the implied design alternatives leads to a final solution which is both ‘optimal’ and acceptable. A methodology which is suitable for this purpose is a mathematical model based on interval arithmetic or interval analysis. The intervals for a set of design parameters form a vector which physically defines a multi-dimensional hypercube; the design problem is then studied by a procedures termed hypercube analysis.