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Axiomatic Design 271

either DP1 or DP2 affect both FR1 and FR2. The design mapping for
this system is given by:

⎧ FR ⎫ ⎡A 11 A 12 ⎤⎡ ⎡ DP ⎤
⎪
1⎪
1
⎨ ⎬ ⎢ ⎥⎢ ⎥ (8.20)
⎪ FR ⎪ ⎢A 21 A 22 ⎥⎢ DP ⎥
⎩
2⎭
2⎦
⎦⎣
⎣
Equation (8.20) is revealing in that the baseline faucet is a coupled
design. The sought design is uncoupled, that is per Axiom 1, an inde-
pendent design with a design matrix where all the diagonal elements
are A’s and all the off- diagonal elements are 0’s. A decoupled design is
usually represented by a triangular design matrix. Uncoupled and
decoupled designs are acceptable per Axiom 1. Coupled designs violate
the Independence Axiom.
8.7.1 Hierarchical level 1 analysis
A valve can be introduced that controls the flow (Q). Additional DPs,
the hot and cold water valves have been connected in a way that a
turn causes one valve to close as the other opens, therefore controlling
the temperature (T). The design equation for this proposed design is
given as:
⎧ FR ⎫ ⎡A 11 0⎤⎡ DP ⎤ ⎤
1⎪
⎪
1
⎨ ⎬ ⎢ ⎥⎢ ⎥ (8.21)
⎥⎢
⎪ FR ⎪ ⎣ 0 ⎢ A 22⎦⎣ DP ⎥
⎩
2⎭
2⎦
This design matrix in Eq. (8.21) is better than the baseline design since
it is functionally uncoupled. However, according to Corollary 3 (App. 8A*),
it is desirable to integrate design in a single physical structure if FRs can
be independently satisfied. The aim is to identify an integration of the
design parameters that would require the two valves.
The desired customer balance between hot and cold water can be
achieved by moving a connecting rod that connects the two valves in
the system where the design parameter for the temperature is the
displacement ‘D’, as illustrated in Fig. 8.20. The connecting rod is
made with adjustable length to control the flow by turning the two
threaded ends of the connecting rod in opposite directions, , hence
Eq. (8.22).
φ
⎧ Q⎫ ⎡ A 0 ⎤ ⎡ ⎤
⎪ ⎪
⎨ ⎬ ⎢ 11 ⎥ ⎢ ⎥ (8.22)
T⎪
D
⎦ ⎣ ⎦
⎩ ⎪ ⎭ ⎢ 0 A ⎥ ⎢ ⎥
⎣
22
*El-Haik (2005)