Mathematical Underpinnings for Achieving Design Functional Requirements

The two types of failure to achieve design functional requirements (FRs) are: Type I, the design cannot hit the FR targets; Type II, it cannot hit them consistently. The causes are due to inter-dependence among the FRs in Type I; and due to build and usage variability of the design in Type II. In this paper, we develop a mathematical understanding for the two types of failures. The underpinnings are Jacobian matrix of FR with respect to input variables for Type I failure; and Jacobian matrix of FR with respect to noise (sources of variability) variables for Type II. Since Independence axiom and Information axiom of Axiomatic Design relate to the interdependence and variability of FRs, the understandings developed herein also serve as the mathematical underpinnings for the two design axioms. The design of snap-fit is used to illustrate the concept and process involved.