ISO 16336:2014

INTERNATIONAL ISO
STANDARD 16336
First edition
2014-07-01
Applications of statistical and related
methods to new technology and
product development process —
Robust parameter design (RPD)
Application de méthodologies statistiques et connexes pour le
développement de nouvelles technologies et de nouveaux produits —
Modèle paramétrique robuste
Reference number
©
ISO 2014
© ISO 2014
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ii © ISO 2014 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions and symbols. 1
3.1 Term and definitions . 1
3.2 Symbols . 3
4 Robust parameter design — Overview . 4
4.1 Requirements . 4
4.2 Assessing the robustness of a system . 4
4.3 Robustness assessment through SN ratio . 6
4.4 An efficient method for assessing technical ideas — Parameter design . 7
4.5 Two-step optimization (Strategy of parameter design) . 8
4.6 Determination of the optimum design .10
5 Assessment of robustness by SN ratio .10
5.1 Concepts of SN ratio .10
5.2 Types of SN ratio .11
5.3 Procedure of the quantification of robustness .11
5.4 Formulation of SN ratio: Calculation using decomposition of total sum of squares .13
5.5 Some topics of SN ratio .19
6 Procedure of a parameter design experiment .20
6.1 General .20
6.2 (Step 1) Clarify the system’s ideal function .20
6.3 (Step 2) Select a signal factor and its range .21
6.4 (Step 3) Select measurement method of output response.21
6.5 (Step 4) Develop noise strategy and select noise factors and their levels .21
6.6 (Step 5) Select control factors and their levels from design parameters .22
6.7 (Step 6) Assign experimental factors to inner or outer array .22
6.8 (Step 7) Conduct experiment and collect data .23
6.9 (Step 8) Calculate SN ratio, η, and sensitivity, S . 23
6.10 (Step 9) Generate factorial effect diagrams on SN ratio and sensitivity .26
6.11 (Step 10) Select the optimum condition .28
6.12 (Step 11) Estimate the improvement in robustness by the gain .28
6.13 (Step 12) Conduct a confirmation experiment and check the gain and “reproducibility” .29
7 Case study — Parameter design of a lamp cooling system .30
Annex A (informative) Comparison of a system’s robustness using SN ratio .40
Annex B (informative) Case studies and SN ratio in various technical fields .47
Bibliography .72
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
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electrotechnical standardization.
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described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
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Attention is drawn to the possibility that some of the elements of this document may be the subject of
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on the ISO list of patent declarations received (see www.iso.org/patents).
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For an explanation on the meaning of ISO specific terms and expressions related to conformity
assessment, as well as information about ISO’s adherence to the WTO principles in the Technical Barriers
to Trade (TBT) see the following URL: Foreword - Supplementary information
The committee responsible for this document is ISO/TC 69, Applications of statistical methods,
Subcommittee SC 8, Application of statistical and related methodology for new technology and product
development.
iv © ISO 2014 – All rights reserved

Introduction
Robust parameter design, also called parameter design, can be applied in product design stage to
identify the optimum nominal values of design parameters based on the assessment of robustness of its
function. Robustness assessment is performed as a consideration of overall loss during the product’s life
cycle. The overall loss is composed of costs and losses at each stage of the product’s life. It includes all the
costs incurred during not only its production stage, but also its disposal stages.
When a product is not robust, the product causes many environmental and social economic losses
(including losses to the manufacturer and the users) due to its poor quality caused by functional
variability throughout its usable lifetime from shipping to final disposal. Product suppliers have
responsibilities and obligations to supply robust products to the market to avert losses and damages
resulting from defects in the products.
The aim of applying parameter design in product design is to prevent defects, failures, and quality
problems that can occur during the usage of the product. A robust product, an output of parameter
design, is a product which is designed in such a way as to minimize user’s quality losses caused by
defects, failures, and quality problems. Note that defects, failures, and quality problems are caused
by functional variability of a non-robust product. In parameter design, optimum nominal values of
a product’s design parameters can be selected by treating a product’s design parameters as control
factors and by assessing robustness under noise factors. The use of parameter design at development
and design stages makes it possible to determine the optimum product design and specification so that
the product is robust in the market.
At manufacturing stage, the product suppliers manufacture their products that meet the product
specifications. One can optimize manufacturing processes to produce the products that meet the
specifications. However, robustness against customer’s environment and products’ aging can be
addressed only by product design.
Robust parameter design methodology provides effective methods for achieving robustness through its
design of specification determination, and it is a preventive countermeasure against various losses in
the market.
In practice, many product’s defects and failures occur due to the product’s response that deviates from
or varies around the designed target values by the change in usage environment and deterioration,
i.e. noise conditions. The variability of product’s response due to noises can be used as a measure of
robustness, because market losses increase in proportion to the magnitude of variability of product’s
response. SN ratio, corresponding to the inverse of the variability measure, is used as a measure of
goodness in robustness. In other words, the higher the SN ratio is, the less the market losses are.
For the experimental plan of parameter design, direct product of inner array and outer arrays is
proposed. Control factors are assigned to the inner array, and signal and noise factors are assigned to
the outer array. By using a direct product plan, all the first level interactions between control factors
and noise factors can be assessed and can be utilized to select the optimum level of control factors from
the point of view of robustness.
Assessing robustness through SN ratio is a key of parameter design. The outer array is for evaluating SN
ratio, robustness, for each combination of levels of control factors indicated by the inner array. The inner
array is for comparing SN ratios and selecting the optimum combination of system’s design parameters.
As for the inner array, an orthogonal array L , is recommended as an efficient plan, and then only
the applications of an orthogonal array L are discussed in this International Standard. Applications
of experimental layout other than orthogonal array L can be found in the examples in references in
the Bibliography. More detailed discussions on inner array and orthogonal arrays can be found in the
references.
Robust parameter design (RPD), and thus this International Standard, is directly targeted at the losses
incurred at the usage stage. Where possible, losses at other stages are also investigated so that the
results of parameter design can be applied to perform the optimum product design for the whole stages
of the product’s life cycle.
INTERNATIONAL STANDARD ISO 16336:2014(E)
Applications of statistical and related methods to new
technology and product development process — Robust
parameter design (RPD)
1 Scope
This International Standard gives guidelines for applying the optimization method of robust parameter
design, also called as parameter design, an effective methodology for optimization based on Taguchi
Methods, to achieve robust products.
This International Standard prescribes signal-to-noise ratio (hereafter SN ratio) as a measure of
robustness, and the procedures of parameter design to design robust products utilizing this measure.
The word “robust” in this International Standard means minimized variability of product’s function
under various noise conditions, that is, insensitivity of the product’s function to the changes in the levels
of noises. For robust products, their responses are sensitive to signal and insensitive to noises.
The approach of this International Standard can be applied to any products that are designed and
manufactured, including machines, chemical products, electronics, foods, consumer goods, software,
new materials, and services. Manufacturing technologies are also regarded as products that are used by
manufacturing processes.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO 3534-1, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in
probability
ISO 3534-3, Statistics — Vocabulary and symbols — Part 3: Design of experiments
3 Terms and definitions and symbols
3.1 Term and definitions
For the purposes of this document, the terms and definitions given in ISO 3534-1 and ISO 3534-3, and
the following apply.
3.1.1
function
work which a system performs in order to fulfil its objective
Note 1 to entry: A function can be expressed by the mathematical form of input-output relation.
3.1.2
robustness
degree of smallness in variability of a system’s function under various noise conditions
Note 1 to entry: System’s performance can be assessed by robustness. SN ratio is a quantitative measure of
robustness.
3.1.3
signal-to-noise ratio
SN ratio
ratio of useful effects to harmful effects in response variations
Note 1 to entry: SN ratio is usually expressed in db value. The notation of db is used instead of dB for SN ratios of
robustness measurements.
Note 2 to entry: The anti-logarithm value of an SN ratio, real number, is the inverse of a variation measure such as
a variance or a coefficient of variation, and inversely proportional to monetary loss.
Note 3 to entry: The change in response caused by intentional change of input signal value is a useful effect. In
case of the ideal function being zero point proportional, the linear slope forced through the zero point is a useful
term.
Note 4 to entry: The change in response caused by noise factors is a harmful effect. Effects of noise factors and
deviation from the ideal function are examples.
Note 5 to entry: SN ratio should contain the variability under noise factors and the discrepancy from the ideal
function under average usage condition.
3.1.4
sensitivity
amount of change in response caused by unit change of input
Note 1 to entry: Sensitivity is usually expressed in db value.
Note 2 to entry: For dynamic characteristic cases, the sensitivity shows the magnitude of linear coefficient due to
input signal, β , where β is a proportional constant.
Note 3 to entry: For the nominal-the-best response, the sensitivity shows the magnitude of mean, m , where m is
an average of responses.
3.1.5
noise
variable which disturbs a system’s function
Note 1 to entry: Any variable in the user’s conditions for operating is either a signal or a noise.
Note 2 to entry: Noise is composed of internal noise and external noise. They are sometimes called as capacity
and demand, respectively. Changes of internal constant of the system or its parts over time, such as deterioration,
aging. and wear, and manufacturing variations are examples of internal noises. Usage conditions and environment
conditions of the product are examples of external noises.
3.1.6
signal
input variable to the system, which is intentionally changed by the user to get an intended value of
response in input-output relation
Note 1 to entry: Any variable in the user’s conditions for operating is either a signal or a noise
Note 2 to entry: There are two kinds of signal: active signal and passive signal. Active signal is operated by user
to get intended response, for example, rotating angle of a steering wheel to change the vehicle’s direction. Passive
signal is used by user to know the value of input from response reading, for example, temperature in thermal
measurement. In both cases, output will change by changing the value of the signal but the user wants to get
response value in the active case, and the user wants to know the value of signal in the passive case.
3.1.7
dynamic characteristics
output response which has multiple ideal target values depending on the value of a signal
Note 1 to entry: The relation between dynamic characteristics and a signal can be expressed by input-output
functional form. The output of a system’s function is dynamic characteristics in many cases.
2 © ISO 2014 – All rights reserved

3.1.8
static characteristics
non-dynamic characteristics
output response which has a fixed target value
Note 1 to entry: Static characteristics can be categorized into three groups depending on the target value; nominal-
the-best, smaller-the-better, and larger-the-better characteristics, where the target value is a finite value, zero,
and infinity, respectively.
3.1.9
inner array
experimental plan where design parameters are assigned as control factors or indicative factors
Note 1 to entry: Each treatment run will be assessed for robustness using SN ratio and sensitivity.
Note 2 to entry: Orthogonal arrays are recommended for the inner array because many design parameters can be
taken into consideration in one set of experiments as control factors.
Note 3 to entry: Experimental factors should be categorized by their roles and assigned separately to inner array
or outer array based on their roles in parameter design. Control factors and indicative factors should be assigned
to the inner array.
3.1.10
outer array
experimental plan where variables in users’ conditions are assigned as noise factors or signal factors for
evaluating SN ratio and sensitivity
Note 1 to entry: Any variable in user’s conditions for operating is either a signal or a noise.
Note 2 to entry: Experimental factors should be categorized by their roles and assigned separately to inner array
or outer array based on their roles in parameter design. Noise factors and signal factors should be assigned to the
outer array.
3.2 Symbols
f degree of freedom
k number of levels of signal factor
L linear form
L linear form for level of i
i
M signal factor/input signal
Mi signal level of i
M value of signal level of i
i
N noise factor
n number of levels of noise factor
Ni noise level of i
p standardized error rate
r sum of squares of input signal levels/effective divisor
S sensitivity
S total sum of squares
T
S sum of squares due to mean
m
S sum of squares due to linear slope β
β
S sum of squares due to the variation of linear slope β between noise levels
N ×β
S sum of squares due to error
e
S estimated value of sensitivity for optimum condition
opt
S estimated value of sensitivity for baseline condition
base
S estimated value of sensitivity for current condition
cur
V variance due to error/error variance
e
V variance due to pooled error/variance due to error and noise
N
y output response
β sensitivity coefficient/linear slope
∆S gain in sensitivity
∆η gain in SN ratio
η SN ratio
η estimated value of SN ratio for optimum condition
opt
η estimated value of SN ratio for baseline condition
base
η estimated value of SN ratio for current condition
cur
ρ standardized contribution ratio
4 Robust parameter design — Overview
4.1 Requirements
Robust parameter design is a rational and efficient assessment for discovering technical means to
improve robustness in the designing process. It is, therefore, necessary to provide the following two
procedures:
a) a procedure for accurate and simple evaluation of robustness;
b) a procedure for efficient assessment of multiple technical means.
This clause provides the approach to the goal of parameter design, and more detailed and specific steps
of a robustness evaluation and a parameter design experiment are described in Clauses 5 and 6.
4.2 Assessing the robustness of a system
How can the robustness of a system be accurately assessed by the SN ratio? The robustness of a system is
associated with many usage conditions of the system, so it cannot be assessed by a simple measurement.
To clarify hidden factors associated with the robustness, the assessment should be approached from the
following two viewpoints.
a) Use of an ideal function: The ideal function is a target function of the system. Actual function of the
system should be measured and compared with the ideal function of the system in the robustness
4 © ISO 2014 – All rights reserved

evaluation. It is important to avoid defects, failure modes, or quality problems for achieving the
ideal function of the system.
b) Use of noise factors: Actual system in usage is working under various noise conditions. Noise
effects should be intentionally introduced in the experiment by changing noise levels and the
actual function of the system should be measured and evaluated under those predetermined noise
conditions. Evaluation of the robustness strongly depends on the choice of noise factors and their
levels. It is essential to apply effective noise strategies.
The function of a system is a work that it performs in order to fulfil its objective. For example, the function
of an electric lamp is to transform electric energy into light energy, and the function of a wind turbine
is to transform natural wind energy into rotating energy to perform a work such as water pumping.
The function is normally expressed in a mathematical functional form of a relationship between input
and output energies. The mathematical functional form can be expressed in many ways. Zero-point
proportional formula is common in energy transformation of real physical systems. The details will be
discussed in Clause 5.
Input and output characteristics are fixed based on the system’s ideal function. Input characteristic is
called as a signal in input-output relationship; this is because the changes in output are acquired by the
user’s intentional changing of the input in real usage and also in the experiment of parameter design. The
signal is associated with energy or information necessary to perform its function. The signal factor is
one of the user’s conditions for changing the input when the users of the system try to control the output
of the system. The signal factor has three or more levels in the experiment for dynamic characteristic
so that the straightness of the actual input-output relationship could be evaluated. There is no signal
factor for static characteristic because it has only one target output. Output characteristic is called as an
output response or simply a response.
It is important to identify a suitable measurement method of output response. In time-dependent
phenomena, for example, detection of output response is difficult in some cases. New measurement
methods should be developed in those cases. The output response is associated with the purpose of a
system. In the case of illumination, for example, the output response is magnitude of light, and in the
case of a water pump, it is quantity of water.
Noise condition is a source that makes the system’s actual function deviate from the ideal function.
Examples include environmental conditions in actual working, such as temperature and humidity, an
actual supplied voltage, electrical noise conditions, frequency of operations, and stress. They are called
as external noises. On the other hand, there are noise conditions which are called internal noises, such
as aging and wear. Examples include operating and/or idling time length after started, deterioration
of system’s parts after long operation, and manufacturing variability of a system and/or its parts.
These noise conditions always reduce the system’s functional performance to lower level than the level
expected at the time of design. Since the purpose of robustness assessment is to clarify the performance
by measuring the extent of this reduction, the variation of the system’s function under noise conditions
should be estimated in robustness evaluation. This is the reason why noise conditions should be
taken into the parameter design experiment as noise factors. Three categories of noise factors are a)
environment, b) aging and changes over time, and c) manufacturing variations. For the effective noise
strategy, various types of noise should be examined in actual usage and environmental conditions.
Figure 1 shows an overview of the evaluation of robustness using a noise factor. Here, multiple data from
X to X should be obtained for the objective system under noise levels, N1 to Nn, and SN ratio η should
1 n
be calculated using the data from X to X as a robustness measure. Formulations of SN ratio are shown
1 n
in Clause 5. When more than two systems are compared, the same levels of the same noise factor should
be applied for all objective systems
Noise factor
Objective system
Data
Noise levels
N1 N2 …NnSN ratio
Evaluated system X X … X η
1 2 n
Ni…Noise level
X …Data
i
Figure 1 — Robustness assessment with a noise factor
When multiple different types of noise factors are applied in an experiment, an orthogonal array can
be applied for determining the noise levels. In Figure 2, noise levels, N1 to Nn, are determined by the
combination of levels of noise factors, such as A, B, and C, indicated by the orthogonal array. Experimental
layout other than orthogonal arrays can be applicable for determining the noise levels.
Orthogonal array for
noise factors
Objective system Data
Noise levels by orthogonal array
123 4… n
A : Ambient temperature, humidity …
B : New product and degraded product…
C : Usage frequency…
Noise level N1 N2 N3 N4 …Nn SN ratio
Evaluated system …
X X X X X η
1 2 3 4 n
A, B, C…Noise factors
Figure 2 — Robustness assessment with noise levels assigned by an orthogonal array
4.3 Robustness assessment through SN ratio
The ideal function and the noise strategy are the key issues for the robustness assessment of robust
parameter design. It is essential to measure and evaluate the variability and efficiency of the actual
function of the system. The intent of doing this is that the evaluation covers the whole technical issues
of the system’s operations to prevent technical problems. Robustness evaluation also involves assessing
the effects of noise factors that inhibit the required function. The results are expressed by SN ratio and
sensitivity.
The SN ratio can discriminate the true difference in robustness between designs. Only relative
comparison of SN ratios is meaningful to perform, because absolute values of SN ratios are affected by
setting levels of noise factors. Thus, it is preferable to perform benchmarking in assessing robustness.
A feature of this approach is that the only information needed to evaluate SN ratios is just that on the
knowledge of the function of the system and the noise conditions. No detailed technical information about
the objective system is needed. SN ratios can be calculated in the same way for the objective systems
as long as they have the same function, that is, the same input-output relationship, even if they have
different technical constituents. Since the robustness of systems can be accurately evaluated through
SN ratios, then the robustness of various systems with different design concepts can be assessed and
compared.
6 © ISO 2014 – All rights reserved

The comparison of various systems based on different technologies or different design concepts can be
performed in the same way through SN ratio. Systems, such as conventional systems and newly developed
systems, one’s own systems and one’s competitor’s systems, can be evaluated and assessed in the same
way through SN ratio, when they have the same function. This is the idea to conduct benchmarking on
various designs in the robustness assessment through SN ratio.
4.4 An efficient method for assessing technical ideas — Parameter design
Basic technologies and mechanisms should be selected as a design concept first to start designing a
system of industrial products. When there are multiple system design concepts to be benchmarked, the
robustness assessment introduced in the previous subclause can be applied to select the best design
concept.
After selecting the best design concept, the next step is to perform a detailed design by selecting values of
system’s design parameters. In this detailed design step, designers can optimize the system by selecting
the optimum nominal values so that the function of the designed system becomes the most robust and
efficient. The system design optimization method performed at this step is called parameter design,
because design optimization is performed by setting design parameters to the optimum nominal values.
Consider what sort of states might be significant. When a system is in the optimum state, it achieves the
best overall performance in all conceivable usage conditions. More specifically, an industrial system can
stably perform its intended function anytime, even when, for example, it is working under a wide range
of temperature and humidity, and when it is used in many different ways and in different environments.
The optimum design conditions are taken as a combination of design parameters’ values that maximize
the robustness of the product. Since optimization by parameter design implies optimizing for maximized
robustness, that is, minimized variability and maximized efficiency, judgments should be made by using
robustness measure, SN ratio, and sensitivity.
The basis of the system design optimization by robustness assessment through SN ratio is a criterion for
optimization in parameter design. The robustness assessment should be performed with regard to all the
possible designs in design space, but in practice this is impossible. This is because a vast number of tests
would have to be performed to take all possible combinations of design parameters into consideration.
As a more practical method for applying in development and design stages, an experiment using an
orthogonal array is recommended where the combinations of many design parameters can be tested
under a limited number of experimental runs. An orthogonal array plan is recommended not only
because it can reduce the number of experimental runs comparing with a full factorial plan with the
same number of control factors, but also because it can assign maximum number of control factors in
a plan under the situation of same number of experimental runs. Reliability of experimental results
should be confirmed in the confirmation experimental run for reproducibility check. Clause 6 describes
a specific method for performing the confirmation experiment to check the reproducibility.
Procedure of a parameter design experiment should be as follows:
— (Step 1) Clarify the system’s ideal function;
— (Step 2) Select signal factor and its range;
— (Step 3) Select measurement method of output response;
— (Step 4) Develop noise strategy, and select noise factors and their levels;
— (Step 5) Select control factors and their levels from design parameters
— (Step 6) Assign experimental factors to inner or outer array;
— (Step 7) Conduct experiment and collect data;
— (Step 8) Calculate SN ratio, η, and sensitivity, S;
— (Step 9) Generate factorial effect diagrams on SN ratio and sensitivity;
— (Step 10) Select the optimum condition;
— (Step 11) Estimate the improvement in robustness by the gain;
— (Step 12) Conduct a confirmation experiment and check the gain and “reproducibility”.
4.5 Two-step optimization (Strategy of parameter design)
Figure 3 presents an overview of parameter design as described above. The experiment in this figure
includes two orthogonal arrays; one orthogonal array for control factors, that is, for design parameters
(inner array) and the other orthogonal array for noise factors (outer array). This layout is called a direct
product plan. The number of experimental data corresponds to the product of the numbers of runs
respectively specified in two orthogonal arrays. For example, in the case of the combination of inner
array, L , and outer array, L , each array has runs of m = 18 and n = 12, and the number of total runs
18 12
comes to 18 × 12 = 216.
Outer
orthogonal array for
noise factors
Inner
orthogonal
Data
array for
control factors
Noise levels by orthogonal array
Noise factors 123 4… n
A : temperature
B : humidity
C : …….
N1 N2 N3 N4 …NnSensitivity SN ratio
1 S η
1 1
2 S η
2 2
3 S η
3 3
4 S η
4 4
… … …
m S η
m m
Figure 3 — Direct product plan for parameter design
Full factorial plan can be used as an outer array plan for noise and signal factors instead of an orthogonal
array plan in some cases. In the case of physical tests, it is recommended to compound many noise
factors into one compounded noise factor. However, it is always recommended to use an orthogonal
array plan as an inner array for design parameters, because many design parameters can be assigned
in one orthogonal array.
The experimental data obtained for each combination of levels of control factors consist of multiple data
with the corresponding number of noise levels. To find out the optimum values of design parameters for
robustness, the sensitivity (mean value in case of nominal-the-best response), and the SN ratio should be
calculated for each row of inner array, that is, for the combination of values of design parameters. Then
8 © ISO 2014 – All rights reserved
Evaluated systems
with assigned
design parameters
the factorial effects of control factors on sensitivity and SN ratio should also be calculated, and they
are summarized in factorial effect diagrams as shown in Figures 4 and 5. Specific calculation formulae
are described in Clause 6. The optimum values of design parameters are selected using the diagrams
on sensitivity and SN ratio. The sensitivity represents the mean value of the data set (in case of static
characteristics), and the SN ratio represents robustness.
The factorial effect diagram shows how the system’s function is affected by each design parameter
incorporated into the experiment. If a factor has a large gradient, it has a large effect on the system’s
function. Two types of factorial effect diagram represent the degree of influence relating to SN ratio and
sensitivity. An important point in two-step design is to pay more attention to SN ratio than to sensitivity.
In the first step, the optimum level of control factor should be selected to maximize SN ratio in the
factorial effect diagram on SN ratio (see Figure 4), and then, in the second step, typically just one design
parameter should be used to adjust a mean value or linear slope, i.e. sensitivity (see Figure 5), to the
target value. For this adjustment, it is desired to select one factor with maximal effect on sensitivity and
minimal effect on SN ratio. The first step is to optimize the design for robustness by SN ratio, and the
second step is to adjust the magnitude to the target value by sensitivity. This two-step design procedure
is a very important concept for the design of robustness. This is the reason why parameter design for
robustness is also called as a two-step optimization.
A1 A2 B1 B2 B3 C1 C2 C3 D1 D2 D3 E1 E2 E3 F1 F2 F3 G1 G2 G3 H1 H2 H3
Figure 4 — Factorial effect diagram on SN ratio (robustness)
-2
-4
-6
A1 A2 B1 B2 B3 C1 C2 C3 D1 D2 D3 E1 E2 E3 F1 F2 F3 G1 G2 G3 H1 H2 H3
Figure 5 — Factorial effect diagram on sensitivity (mean value or linear slope)
Why is the two-step optimization important? Which is more difficult, the robustness optimization by SN
ratio or the magnitude adjustment by sensitivity?
The order of the optimizations is important to design a robust system efficiently. Consider an example
of the case of voice recording. If audio data are recorded with high background noise, then adjusting the
volume will hardly make the recorded sound any easier to listen to when it is played back. To extract
SN ratio (db)
Sensitivity (db)
information buried in the noise, techniques such as noise reduction to cancel the effects of noises or
using a microphone that is less sensitive to the background noise shall be employed. Improving SN ratio
requires advanced technical ability and counter-measures in recording. On the other hand, when the
average recording level is too low, it can easily be improved by adjusting the volume during playback.
The controlling of the average value of the playback sound by a volume can often be accomplished by a
relatively simple method in this way. Adjusting the magnitude can be performed by sensitivity.
Another example is visual imaging function such as photographs and video pictures. The average tone
level can easily be corrected, but a picture taken in dark conditions is often very noisy and results in
a low-quality picture. There are also limits to how much the picture quality can be improved by image
processing.
It is relatively easy to achieve adjusting the magnitude, because it needs just one adjusting parameter.
It is easy to adjust the average energy level. On the other hand, it is not easy to improve robustness. It
is desired to have as many control factors as possible. In designing a system, it is therefore wise to give
greater priority to setting the optimum levels of design parameters to maximize SN ratio. This forms
the foundation of the two-step optimization, where robustness optimization by the SN ratio should have
the first priority.
4.6 Determination of the optimum design
Once parameter design experiment clarifies which design parameters affect SN ratio and which design
parameters affect sensitivity as in factorial effect diagrams, one can select a set of optimum values
of design parameters based on robustness. Then, the final optimum design can be determined by
considering other constraints such as cost and delivery requirements.
Since a system’s final optimum design should be determined by the overall balance of many constraints,
it is preferable to select an experimental plan where each experimental factor covers a wider range in a
design space. There is a possibility that the optimum value might exist in the range far from experiences;
then it is recommended that the levels of control factors should cover a range as widely as possible.
In the parameter design, robustness optimization is performed through maximizing SN ratio. The SN
ratio is a quantitative measure of the user’s quality loss due to defects, failures, and quality problems
caused by lack of robustness. The user’s quality loss can include losses by malfunctions, by defects, by
additional maintenance costs, etc.
According to Taguchi’s quality loss function, the SN ratio can be transformed to user’s quality loss in
monetary unit. Total loss to the society caused by the product can be derived from the user’s quality
loss by adding other cost, such as product development cost, material cost, production cost, shipping
cost, normal maintenance cost, disposal cost, etc. The total social loss should be a quality measure
of the product. In product design stage, a product designer should consider the total social loss from
the viewpoint of technology. However, it is difficult for the designer to forecast the total social loss in
the design stage, but he should, at least, assess and optimize the product design from the viewpoint of
robustness. Robust parameter design focuses on the user’s quality loss from the viewpoint of robust
engineering, that is, the variability in function of the product.
5 Assessment of robustness by SN ratio
5.1 Concepts of SN ratio
The variability in function of a system should be evaluated and optimized through parameter design
for designing a robust product. When a subsystem is to be assessed for robustness, one should consider
noise conditions at the whole system level in the users’ hand. It is critical to ensure the robustness at
whole system level.
A system’s function can be defined as a functional form of input-output relationship at usage stage
of the system. Users manipulate a signal to get an intended output response of the system. Signal is
an input characteristic that is intentionally set to change the output of the system. A functional form
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that represents the ideal input-output relationship of the system’s function is called as a system’s ideal
fun
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