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Qualitative Axiomatic Design

Qualitative axiomatic design is an informal version of Suh's Axiomatic Design.

DRAFT - needs to be cleaned up and expanded.

Nam P. Suh invented a design method called axiomatic design (AD). The key references are [Suh90] and [Suh01].

AD is a very systematic way of developing a design. If one leans to such methods, then axiomatic design could be very useful.

However, AD can also be useful in a more qualitative and informal way.

AD is based on only two axioms:

The Independence Axiom: Keep the functional requirements independent of one another.
The Information Axiom: Minimize the information content of a design.

In AD, a functional requirement (FR) is more loosely defined than it is here (see functional requirement). A FR in AD is basically any requirement, including constraints. It is not clear if this is the best approach, but it certainly does seem to work as an element of AD.

Furthermore, one aspires to find a single design parameter (DP) – some characteristic of the product – the value of which determines whether the design satisfies a single given FR. One DP for each FR. This is rarely possible, but it is the ideal toward which one should work.

Also, information is typically considered a quantitative value in AD – one can actually calculate the number of information bits in a design.

The axioms are more than just the foundation of AD, though. They are very useful principles that can be applied generally during design.

The Independence Axiom requires FRs to be independent. This means that changing the value of a DP will affect only the FR it is meant to satisfy. But more broadly, it can guide a designer in specifying requirements.

The Information Axiom really amounts to saying simple designs are better than complex ones. Complex designs have more information in them; simple ones have less.

Here is a short example to demonstrate these ideas.

Problem: An existent paint mixing machine is arranged as follows:

  • Two tanks hold paint to be mixed.
  • Each tank has a pump; each pump is driven by a separate motor.
  • The pumps deliver component paints into a mixing element that mixes the paints and pours the paint into cans.
  • Different cans of paint are coming out in slightly different shades due to small variations in the speeds of the two motors. This is unacceptable.

There are two FRs here:

  1. produce mixed paint at defined rates, and
  2. produce the right colour paint in every can.

There are two DPs here: the speeds of the two motors driving the pumps.

With respect to these DPs, the FRs are not independent. Changing the speed of one motor will affect both FRs. In the terminology of AD, this design is coupled.

One rather unimaginative solution is to implement some active, dynamic control system that will constantly sense the actual speed of the pumps and make micro-adjustments of the motor speeds to keep mixed paint coming at the right rate and the right colour.

But this is a problematic solution: it requires a significant investment in sensitive electronic equipment in a very dirty environment; complexity increases, and so does cost; reliability decreases; more training is needed….

There is a better solution, that is purely mechanical (or nearly so). Instead of using two motors, use one motor and a gearbox. The gearbox allows the two pumps to be driven at different rates by a single source. So the relative variation between motors is eliminated. Now there are two different DPs: the speed of the motor, and the ratio of the gearbox.

The speed of the motor defines the rate at which paint is produced, and the gearbox ratio defines the shade of paint produced. In this case, the FRs are independent with respect to the new DPs.

So by keeping the FRs independent (with respect to the DPs) we have a better solution: it is more robust, will work better in a dirty environment, and will cost less to operate, etc.

References

design/qualitative_axiomatic_design.txt · Last modified: 2020.03.12 13:30 (external edit)