Method to determine process input variables' values that optimally balance customer based probability of achieving quality and costs for multiple competing attributes
A method for balancing competing attributes in a multi-attribute design optimization, which receives attributes and a set of input variables as inputs, and incorporates the variation of the input variables, is disclosed. The method receives transfer functions for the performance as a function of the input variables and for the customer assessment of the performance attributes. A preference function is constructed for each of a plurality of attributes to be balanced, the preference function defining a preferred outcome for a given set of inputs. The preference functions associated with each attribute are aggregated to define an aggregated preference function, thereby integrating the attributes. Optimal values are calculated for the set of input variables that optimize the aggregated preference function.
1 . A method for balancing competing attributes in a multi-attribute design optimization, which receives attributes and a set of input variables as inputs, the method comprising:
constructing a preference function for each of a plurality of attributes to be balanced, the preference function defining a preferred outcome for a given set of inputs; aggregating the preference functions associated with each attribute to define an aggregated preference function, thereby integrating the attributes; and
calculating optimal values for the set of input variables that optiize the aggregated preference function.
2 . The method of claim 1 , which receives as inputs a performance transfer function and variation data and a customer transfer function, the method further comprising:
determining a probability distribution of obtaining a performance level for each attribute based upon the performance transfer function and variation data; and
representing the customer transfer function as a probability distribution of achieving customer quality based upon performance attribute values.
3 . The method of claim 2 , further comprising:
determining a probability that customer determined quality will be achieved based upon each of the performance level probability distributions and the customer-driven transfer function.
4 . The method of claim 1 , wherein the constructing a preference function comprises at least one of:
constructing a customer quality performance preference function for each attribute; constructing a manufacturing preference function for each attribute; and
constructing a design alternatives preference function for each attribute.
5 . The method of claim 4 , wherein:
the constructing a preference function comprises at least two of:
constructing a customer quality performance preference function for each attribute;
constructing a manufacturing preference function for each attribute; and
constructing a design alternatives preference function for each attribute;
the method further comprises aggregating the aggregated preference functions to define a grand aggregated preference function; and
the calculating comprises calculating a set of input variables that optimize the grand aggregated preference function.
6 . The method of claim 1 , further comprising:
generating a predicted distribution for performance based upon the calculated input variables.
7 . The method of claim 1 , further comprising:
generating a predicted probability for achieving customer determined quality based upon the calculated input variables.
8 . The method of claim 1 , further comprising:
generating a predicted impact on cost and revenue based upon the calculated input variables.
9 . The method of claim 1 , wherein:
the constructing a preference function comprises constructing a preference function h(r) of the form:
h
(
r
)
=
2
1
+
(
i
n
3
)
(
1
-
r
1
-
R
)
where:
r is equal to the Probability of Achieving Quality; and
R is equal to a reference probability.
10 . The method of claim 1 , wherein:
the aggregating the preference functions for each attribute comprises aggregating the preference functions for two performance attributes h[(h 1 ,w 1 ),(h 2 ,w 2 )] according to the form:
h
[
(
h
1
,
w
1
)
,
(
h
2
,
w
2
)
]
=
(
w
1
h
1
s
+
w
2
h
2
s
w
1
+
w
2
)
1
/
s
where:
h 1 is equal to a first attribute
w 1 is equal to a weight for the first attribute
h 2 is equal to a second attribute; and
w 2 is equal to a weight for the second attribute.
11 . The method of claim 1 , wherein:
the calculating occurs in the absence of given targets for output attributes.
12 . The method of claim 1 , wherein:
the calculating comprises a global optimization technique based on the aggregated preference function.
13 . The method of claim 17 wherein:
the constructing a preference function comprises determining a customer-driven weight for each attribute.
14 . The method of claim 8 wherein:
the generating a predicted impact on cost and revenue comprises determining a change in purchase behavior function, dependent upon determining a customer-driven weight for each attribute.
15 . The method of claim 1 , wherein:
the calculating optimal values for a set of input variables further comprises calculating optimal values for a set of input variables that include distribution-characterizing parameters that optimize the aggregated preference function.
16 . The method of claim 15 , wherein:
the distribution-characterizing parameters include both nominal and standard deviation values for the set of input variables.
17 . A prog storage device readable by a machine, the device embodying a program or instructions executable by the machine to perform the method of claim 1 .