Page 307 - Design for Six Sigma a Roadmap for Product Development

Axiomatic Design 277

their corresponding measures for each of the non-zero
sub-matrices.
Theorem 11: (Invariance)
Reangularity, R, and Semangularity, S, for a design
matrix [DM] are invariant under alternative orderings
of the FR and DP variables, as long as orderings preserve
the association of each FR with its corresponding DP.
Theorem 12: (Sum of Information)
The sum of information for a set of events is also infor-
mation, provided that proper conditional probabilities
are used when the events are not statistically
independent.
Theorem 13: (Information Content of the Total System)
If each DP is probabilistically independent of other DPs,
the information content of the total system is the sum
of the information of all individual events associated
with the set of FRs that must be satisfied.
Theorem 14: (Information Content of Coupled versus Uncoupled Designs)
When the state of FRs is changed from one state to
another in the functional domain, the information
required for the change is greater for a coupled process
than for an uncoupled process.
Theorem 15: (Design-Manufacturing Interface)
When the manufacturing system compromises the inde-
pendence of the FRs of the product, either the design of
the product must be modified, or a new manufacturing
process must be designed and/or used to maintain the
independence of the FRs of the products.
Theorem 16: (Equality of Information Content)
All information content that is relevant to the design
task is equally important regardless of their physical ori-
gin, and no weighing factor should be applied to them.

A.3 Theorems for design of large systems

Theorem 17: (Importance of High Level Decisions)
The quality of design depends on the selection of FRs and
the mapping from domains to domain. Wrong decisions
made at the highest levels of design hierarchy cannot be
rectified through the lower level design decisions.