Compound Noise - MIT Department of Mechanical Engineering

392 J. SINGH ET AL.
System
Table II. Results from resolution III control and noise factor array
Hierarchy
Measure
of sparsity
of effects
Number of
replications
Matching of
all control
factors with
their robust
setting
(%)
Matching of
control factors
with their
robust setting
(%)
Improvement
ratio
(%)
Op Amp Strong 0.105 100 98 99.6 99.91
CSTR Weak 0.647 100 None 76.5 96.5
Temperature Weak 0.725 100 28 55 87
control circuit
Slider crank Weak 0.119 100 91 95.5 97.6
System
Table III. Results from resolution III control factor array and two-level compound noise
Hierarchy
Measure of
sparsity of
effects
Number of
replications
Matching of
all control
factors with
their robust
setting
(%)
Matching of
control factors
with their
robust setting
(%)
Improvement
ratio
(%)
Improvement
ratio (from
resolution III
noise array)
(%)
Op Amp Strong 0.105 100 86 97.2 99.37 99.91
CSTR Weak 0.647 100 None 41.17 39.8 96.5
Temperature Weak 0.725 100 None 43.5 25.2 87
control circuit
Slider crank Weak 0.119 100 89 94 96.5 97.6
System
Table IV. Average results from full factorial control factor array and two-level random compound noise
Hierarchy
Measure of
sparsity of
effects
Number of
replications
Matching of
all control
factors with
their robust
setting
(%)
Matching of
control factors
with their
robust setting
(%)
Improvement
ratio
(%)
Improvement
ratio (from
Taguchi’s
compound
noise)
(%)
Op Amp Strong 0.105 1000 30.8 73 80.2 99.2
PNM Strong 0.132 2 4 = 16 50 68.75 79.9 99.5
Journal bearing Strong 0.28 2 3 = 8 100 100 100 98.84
CSTR Weak 0.647 2 6 = 64 54.69 70.3 67.6 58.4
Temperature Weak 0.725 2 5 = 32 68.75 76.56 74.75 30.65
control circuit
Slider crank Weak 0.119 2 5 = 32 50 70 55.2 98.5
The compound noise strategy also does not perform well with a resolution III control factor array for the
temperature control circuit. The improvement ratio drops from 87% for a resolution III noise array to 25%
for two-level compound noise.
In the formulation of compound noise as suggested by Taguchi 1 and Phadke 3 , we need to know the
directionality of noise factors on the system’s response. We need to run some fractional factorial experiments
on the system to gather information about the directionality of noise factors. We tried a different formulation
Copyright c○ 2006 John Wiley & Sons, Ltd. Qual. Reliab. Engng. Int. 2007; 23:387–398
DOI: 10.1002/qre