30-05-2012, 12:38 PM
Robust Design and Taguchi Methods
[attachment=23500]
In general, the higher the performance measure the better.
Because of the need to estimate s2, we are led to designs with two aspects.
First one creates a design with design parameters, called by Taguichi the Inner
Array. Then one creates the array of noise factors, called by Taguichi the Outer
Array. Thus for each setting in the design matrix, one runs one run for each setting
in the noise matrix. The measurements of the performance characteristic are then
grouped to give the performance statistic for that run of the design matrix.
The Inner Array is generally a nearly-saturated array, usually a fractional factorial
or Plackett-Burman design. The same kind of designs are used for for the
Outer Array.
In the analysis, we’ll look for factors that affect the targeted response only,
those that affect variability only, those that affect both, and those that affect neither.
Let’s consider an example from Bell Labs. The first step in silicon wafer fabrication
is the growth of a smooth epitaxial layer onto a polished silicon wafer.
The epitaxial layer is deposited on wafers while they are mounted on a rotating
spindle called a susceptor. The problem: high drop-out rate caused by deviation in
thickness, both between and within wafers, from the target value of 14.5 microns.
Objective: reduce nonuniformity of epitaxial layer, and keep average thickness
close to 14.5 microns. List responses: Epitaxial thickness, with a target value of
14.5 microns, a current average of 14.5, and a current std dev of 0.4. Control
parameters: susceoptor rotation direction, arsenic flow rate, deposition time, nozzle
position, and deposition temperature. List noise: uneven temperature in Bell
Jar, nonuniform vapor concentration, nonuniform vapor composition, deviation in
control parameter settings.
Improving Robust Design from a statistical point of view
Experimental Designs. Although the designs for the inner array and the
outer array are economical individually, when they are crossed together they are
not as economic.
For example, consider the crossed array when control factors A, B, C, in a
23
[attachment=23500]
In general, the higher the performance measure the better.
Because of the need to estimate s2, we are led to designs with two aspects.
First one creates a design with design parameters, called by Taguichi the Inner
Array. Then one creates the array of noise factors, called by Taguichi the Outer
Array. Thus for each setting in the design matrix, one runs one run for each setting
in the noise matrix. The measurements of the performance characteristic are then
grouped to give the performance statistic for that run of the design matrix.
The Inner Array is generally a nearly-saturated array, usually a fractional factorial
or Plackett-Burman design. The same kind of designs are used for for the
Outer Array.
In the analysis, we’ll look for factors that affect the targeted response only,
those that affect variability only, those that affect both, and those that affect neither.
Let’s consider an example from Bell Labs. The first step in silicon wafer fabrication
is the growth of a smooth epitaxial layer onto a polished silicon wafer.
The epitaxial layer is deposited on wafers while they are mounted on a rotating
spindle called a susceptor. The problem: high drop-out rate caused by deviation in
thickness, both between and within wafers, from the target value of 14.5 microns.
Objective: reduce nonuniformity of epitaxial layer, and keep average thickness
close to 14.5 microns. List responses: Epitaxial thickness, with a target value of
14.5 microns, a current average of 14.5, and a current std dev of 0.4. Control
parameters: susceoptor rotation direction, arsenic flow rate, deposition time, nozzle
position, and deposition temperature. List noise: uneven temperature in Bell
Jar, nonuniform vapor concentration, nonuniform vapor composition, deviation in
control parameter settings.
Improving Robust Design from a statistical point of view
Experimental Designs. Although the designs for the inner array and the
outer array are economical individually, when they are crossed together they are
not as economic.
For example, consider the crossed array when control factors A, B, C, in a
23