# Quality Progress - February 2018 - 25

```A design concept that satisfies
axioms one and two overcomes the
design's conceptual vulnerabilities.

FIGURE 2

Manufacturing process requiring a
control system

A poor design concept

Chemical B

Reactor

Chemical A

FIGURE 3

Coupling design concept

[ ][

][ ]

FR1 = A11 × DP1 + A12 × DP2
FR 2 = A 21 × DP1 + A 22 × DP2

Chemical B

DP2

DP1

Continuing the example from earlier,
the first design concept the design
team proposes to the customer is
to install a valve on each pipe that
carries chemicals A and B to the
reactor, as illustrated in Figure 3. In
this design, the first DP is valve one
turning and the second DP is valve
two turning.
Based on the data from regression
analysis and design of experiment
(DoE), the design team develops
transfer functions that correlate FRs
and DPs:
FR1
DP1
A A12
= 11
FR 2
DP2
A 21 A 22
In a matrix, numbers are arranged
in rows and columns. Multiplying
two matrixes is possible only when
the number of columns in the left
matrix-the coefficient matrix in this
example-is the same as the number
of rows in the right matrix-the DP
matrix. The equation above can be
separated into two equations:

Reactor

If the customer turns either valve
one or valve two to change the total
flow rate of A + B (FR1), it inevitably
changes the A/B ratio (FR 2), as well.
Therefore, FRs in this design concept are not independent from each
other-they are coupled with each
other. This design lacks robustness
at the conceptual level because it
violates axiom one. The sign of a
coupling design is a full or almost full
coefficient matrix in its matrix transfer
function equation.

Chemical A

The improved design
DP = design parameter

To uncouple the two FRs, the design
team develops a new design concept
in which there is a 1:1 relationship
between FRs and DPs. In this concept,

qualityprogress.com ❘ February 2018

QP 25

```
http://www.qualityprogress.com

Seen and Heard
Progress Report
Career Coach
Office Efficiency
The Crown Jewels of Design
Open Lines
Less Is More
ASQ 2018 Six Sigma Resource Guide
Standard Issues
Six Sigma Solutions
Statistics Spotlight
Marketplace
Footnotes
Try This Today
Quality Progress - February 2018 - intro
Quality Progress - February 2018 - cover1
Quality Progress - February 2018 - cover2
Quality Progress - February 2018 - 1
Quality Progress - February 2018 - 2
Quality Progress - February 2018 - 3
Quality Progress - February 2018 - 4
Quality Progress - February 2018 - 5
Quality Progress - February 2018 - Seen and Heard
Quality Progress - February 2018 - 7
Quality Progress - February 2018 - Expert Answers
Quality Progress - February 2018 - 9
Quality Progress - February 2018 - Progress Report
Quality Progress - February 2018 - 11
Quality Progress - February 2018 - Mr. Pareto Head
Quality Progress - February 2018 - 13
Quality Progress - February 2018 - Career Coach
Quality Progress - February 2018 - 15
Quality Progress - February 2018 - Office Efficiency
Quality Progress - February 2018 - 17
Quality Progress - February 2018 - 18
Quality Progress - February 2018 - 19
Quality Progress - February 2018 - 20
Quality Progress - February 2018 - 21
Quality Progress - February 2018 - The Crown Jewels of Design
Quality Progress - February 2018 - 23
Quality Progress - February 2018 - 24
Quality Progress - February 2018 - 25
Quality Progress - February 2018 - 26
Quality Progress - February 2018 - 27
Quality Progress - February 2018 - 28
Quality Progress - February 2018 - 29
Quality Progress - February 2018 - Open Lines
Quality Progress - February 2018 - 31
Quality Progress - February 2018 - 32
Quality Progress - February 2018 - 33
Quality Progress - February 2018 - 34
Quality Progress - February 2018 - 35
Quality Progress - February 2018 - 36
Quality Progress - February 2018 - 37
Quality Progress - February 2018 - Less Is More
Quality Progress - February 2018 - 39
Quality Progress - February 2018 - 40
Quality Progress - February 2018 - 41
Quality Progress - February 2018 - 42
Quality Progress - February 2018 - 43
Quality Progress - February 2018 - ASQ 2018 Six Sigma Resource Guide
Quality Progress - February 2018 - 45
Quality Progress - February 2018 - Standard Issues
Quality Progress - February 2018 - 47
Quality Progress - February 2018 - 48
Quality Progress - February 2018 - 49
Quality Progress - February 2018 - Six Sigma Solutions
Quality Progress - February 2018 - 51
Quality Progress - February 2018 - 52
Quality Progress - February 2018 - Statistics Spotlight
Quality Progress - February 2018 - 54
Quality Progress - February 2018 - 55
Quality Progress - February 2018 - 56
Quality Progress - February 2018 - 57
Quality Progress - February 2018 - Marketplace
Quality Progress - February 2018 - 59
Quality Progress - February 2018 - Footnotes
Quality Progress - February 2018 - 61
Quality Progress - February 2018 - 62
Quality Progress - February 2018 - 63
Quality Progress - February 2018 - Try This Today
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