Page 124 - Design for Six Sigma a Roadmap for Product Development

Product Development Process and Design for Six Sigma 99

The independent variables may be the DPs or the PVs according to the
mapping of interest and where the solution is sought. A “change” can
be either soft or hard. Soft changes imply adjusting the nominal val-
ues within the specified tolerances, changing the tolerance ranges, or
both. Hard changes imply eliminating or adding DPs or PVs in the
concerned mapping and accordingly their subsequent soft changes. For
example, in manufacturing, soft process changes can be carried out by
parametric adjustment within the permitted tolerances while hard
changes may require PV alteration. On the redesign side, design
changes to reduce or eliminate a detrimental behavior of an FR may
call for dramatic changes in both the design entity and manufacturing
processes when soft changes cannot produce the desired result.
Mathematically, let the concerned FR (CTS) be expressed using y f(x)
as FR f(DP), where DP is an array of mapped-to DPs of size m. Let
each DP in the array be written as DP i g(PV i ), where PV i ,i 1,…,m
is an array of process variables that are mapped to DP i . Soft changes may
be implemented using sensitivities in physical and process mappings.
Using the chain rule, we have

∂FR ∂FR

f ′ [ g(PV i )] g′(PV ij ) (3.1)
∂DP i
∂PV ij ∂DP i ∂PV j
where PV ij is a process variable in the array PV i that can be adjusted
(changed) to improve the problematic FR. The first term represents a
design change; the second, a process change. An efficient DFSS
methodology should utilize both terms if all FRs are to be released at
Six Sigma performance levels.

3.10 What Kinds of Problems Can Be
Solved by DFSS?
A design entity of a process or a product can be depicted in a P-diagram
as in Fig. 3.19. The useful output is designated as the array of FRs y,
which in turn is affected by three kinds of variables: the signals rep-
resented by the array m, the design parameters represented by the
array x, and the noise factors represented by array z. Variation in y
and its drift from its targeted performance are usually caused by the
noise factors. The norms of m and y arrays are almost equal when they
are expressed in terms of energy in dynamic systems. In this context,
the objective of DFSS is to reduce the difference array norm | |
|y| |m| between both array norms to minimum, when the target
is zero, and reduce the variability around that minimum. Variability
reduction can be achieved by utilizing the interaction x
z. In a DFSS
project, we are concerned with an FR, say, y j , which suffers from