Hubcap and ignition switch designs - case studies in Independence Axiom

Independence Axiom offers designers a guide to good design. It declares that the design parameters (DPs) conceived for a good design must maintain the independence of the design functional requirements (FRs). Specifically, by relating FRs to DPs through a design matrix [DM] with elements ∂FRi/∂DPj, Independence Axiom declares that only designs with diagonal or triangular design matrix can maintain the functional independence of FRs; and that they should be the only acceptable ones. Starting with the formal definition of functional independence, we derive the criterion for functional independence of FRs as the Jacobian determinant | J | ≠ 0; where the Jacobian matrix [ J ] is shown to be identically equal to [DM]. We further show that if and only if | J | ≠ 0 can the design FRs achieve their target values. Thus the criterion | J | ≠ 0 substantiates the declaration of Independence Axiom since determinant of a diagonal or triangular design matrix is not equal to zero. It serves as the mathematical basis for teaching and implementing Independence Axiom in design. Two case studies are presented to illustrate the implementation of Independence Axiom via the Jacobian determinant | J |