ISO/FDIS 16337
(Main)Application of statistical and related methods to new technology and product development process -- Robust tolerance design (RTD)
Application of statistical and related methods to new technology and product development process -- Robust tolerance design (RTD)
Application des méthodes statistiques et des méthodes liées aux nouvelles technologies et de développement de produit -- Plans d'expériences robustes
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DRAFT INTERNATIONAL STANDARD
ISO/DIS 16337
ISO/TC 69/SC 8 Secretariat: JISC
Voting begins on: Voting terminates on:
2019-11-08 2020-01-31
Application of statistical and related methods to new
technology and product development process — Robust
Tolerance Design (RTD)
Application des méthodes statistiques et des méthodes liées aux nouvelles technologies et de développement
de produit — Plans d'expériences robustesICS: 03.120.30
THIS DOCUMENT IS A DRAFT CIRCULATED
FOR COMMENT AND APPROVAL. IT IS
THEREFORE SUBJECT TO CHANGE AND MAY
NOT BE REFERRED TO AS AN INTERNATIONAL
STANDARD UNTIL PUBLISHED AS SUCH.
IN ADDITION TO THEIR EVALUATION AS
BEING ACCEPTABLE FOR INDUSTRIAL,
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Reference number
NATIONAL REGULATIONS.
ISO/DIS 16337:2019(E)
RECIPIENTS OF THIS DRAFT ARE INVITED
TO SUBMIT, WITH THEIR COMMENTS,
NOTIFICATION OF ANY RELEVANT PATENT
RIGHTS OF WHICH THEY ARE AWARE AND TO
PROVIDE SUPPORTING DOCUMENTATION. ISO 2019
---------------------- Page: 1 ----------------------
ISO/DIS 16337:2019(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2019
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting
on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address
below or ISO’s member body in the country of the requester.ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Fax: +41 22 749 09 47
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2019 – All rights reserved
---------------------- Page: 2 ----------------------
ISO/DIS 16337:2019(E)
Contents Page
Foreword ........................................................................................................................................................................................................................................iv
Introduction ..................................................................................................................................................................................................................................v
1 Scope ................................................................................................................................................................................................................................. 1
2 Normative references ...................................................................................................................................................................................... 1
3 Terms and definitions ..................................................................................................................................................................................... 1
4 Robust tolerance design ............................................................................................................................................................................... 1
4.1 General ........................................................................................................................................................................................................... 1
4.2 RTD experiment ..................................................................................................................................................................................... 4
4.2.1 Objective system .............................................................................................................................................................. 4
4.2.2 Experimental design ..................................................................................................................................................... 4
4.2.3 Analysis of variance of data of RTD experiment ................................................................................... 6
4.3 Tolerance determination .............................................................................................................................................................10
4.3.1 Estimating total variance when tolerance is changed ..................................................................10
4.3.2 Deciding tolerance .......................................................................................................................................................11
5 Case studies of RTD (1): a constant voltage circuit with theoretical formula....................................12
5.1 RTD experiment for the circuit ..............................................................................................................................................12
5.1.1 Objective system ...........................................................................................................................................................12
5.1.2 Experimental design for the circuit ..............................................................................................................13
5.1.3 Data collection and ANOVA ..................................................................................................................................14
5.2 Tolerance determination .............................................................................................................................................................16
6 Case study (2): Reliability of piston-lip by simulation experiment ..............................................................18
6.1 RTD experiment for the piston-lip ......................................................................................................................................18
6.1.1 Objective system and experimental design ...........................................................................................18
6.1.2 Data collection and ANOVA ..................................................................................................................................19
6.2 Tolerance determination .............................................................................................................................................................20
Bibliography .............................................................................................................................................................................................................................26
© ISO 2019 – All rights reserved iii---------------------- Page: 3 ----------------------
ISO/DIS 16337:2019(E)
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
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.The procedures used to develop this document and those intended for its further maintenance are
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
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/patents).Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.For an explanation on the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following
URL: www .iso .org/iso/foreword .html.This document was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 8, Application of statistical and related methodology for new technology and product
development.iv © ISO 2019 – All rights reserved
---------------------- Page: 4 ----------------------
ISO/DIS 16337:2019(E)
Introduction
A designer of a product decides the specification of the product, and hands it to manufacturing process
for manufacturing. The specification includes the designed nominal values and tolerances of the
parts or elements of the product. The optimum nominal values of design parameters are determined
by Robust Parameter Design (RPD), and the optimum tolerances of them are determined by Robust
Tolerance Design (RTD).RPD described in ISO 16336 is applied to the objective product prior to RTD. In RPD, major noise factors
are taken to evaluate robustness, that is, SN-ratio. SN-ratio represents the variability of the output of
the product. SN-ratio is a measure of comparison of robustness between levels of control factors.
RTD described in this document is the method of selecting the degree of errors of the parts or elements
of the product from the viewpoint of variability under the RPD-optimum condition, that is, the
combination of optimum designed values of design parameters. If a manufactured product has some
errors from the designed values of design parameters, the output of the product is deviated from the
designed value. The error of design parameter should be smaller than the designed tolerance to keep
the output of the product within the designed variability. This is the reason why the design parameter
needs a tolerance.The design of a product can be finalized by setting optimum tolerances of design parameters by RTD.
The realistic variance of the product manufactured with errored parts or elements can be estimated
in RTD. After RPD finds out a set of optimum values of design parameters, RTD is applied to check that
actual variance is smaller than the target variance under the RPD-optimum condition.
RPD can set the optimum nominal values of design parameters without cost-up, but RTD is closely
related to manufacturing cost. Smaller tolerances, that means higher-grade parts or elements, lead
to cost-up, and larger tolerances, that means lower-grade parts or elements, lead to cost-down. To
finalize the product design process, cost of manufacturing the product is considered. Loss function of
Taguchi Methods is applied to transform the merits of improvement in quality to money scale as same
as cost. The cost of improvement and the merits of improvement in quality are balanced in deciding the
tolerances. Both of RPD and RTD give cost effective way of optimizing the design of product.
When RPD cannot realize the target variability of the product, smaller tolerances of the design
parameters are applied to improve the variability, but smaller tolerances lead to cost-up.
On the other hand, when RPD can realize variability much smaller than the target variability, larger
tolerances of design parameters are applied to save the manufacturing cost of the product, then larger
tolerances lead to cost-down.The product manufactured based on the combination of the optimum nominal values and tolerances
of the design parameters is robust to noise conditions in users’ stage of it. Robust product minimizes
users’ quality losses caused by defects, failures and quality problems.© ISO 2019 – All rights reserved v
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DRAFT INTERNATIONAL STANDARD ISO/DIS 16337:2019(E)
Application of statistical and related methods to new
technology and product development process — Robust
Tolerance Design (RTD)
1 Scope
This document specifies guidelines for applying the Robust Tolerance Design (RTD) of Taguchi Methods
to finalize the design process of products.Robust Tolerance Design (RTD) is applied to the objective product to set the optimum tolerances of
design parameters around the nominal values. RTD finds the effects of errors in design parameters on
final product’s output and estimates the total variance of the output when tolerances are changed. RTD
achieves the target variance of the output from the viewpoints of robustness, performance and cost.
Tolerance expresses a maximum allowable error in the value of design parameter in manufacturing
process. It is perfect that parts or elements of every product have the designed nominal values of the
design parameters. However, actual manufacturing cannot give the exact designed values of the design
parameters for all the products. The actual products have some errors in the values of parts or elements
of the products. These errors are supposed to be within the designed tolerances in manufacturing.
This document is applicable to determine the optimum tolerances and finalize the design process of the
product.2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 16336 apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
• IEC Electropedia: available at http: //www .electropedia .org/• ISO Online browsing platform: available at http: //www .iso .org/obp
3.1 tolerance
difference between a nominal value and its allowable limit.
3.2 robust tolerance design (RTD)
a method of setting optimum tolerances from the viewpoints of robustness, performance and cost.
4 Robust tolerance design4.1 General
A product design section gives a specification of a product, that is, the nominal values and tolerances of
design parameters, to manufacturing section. Manufacturing sections keeps the designed specification
© ISO 2019 – All rights reserved 1---------------------- Page: 6 ----------------------
ISO/DIS 16337:2019(E)
for every product. When a specification of a design parameter specifies the limits as m±Δ , the design
parameter’s value x in manufacturing process satisfies the following restriction;
mx−≤ΔΔ≤+m ,where m and Δ denote a nominal value and its tolerance respectively.
If absolute error of a design parameter is larger than the tolerance Δ, the variability of the product
cannot keep the designed performance and specification.Robust Tolerance Design (RTD) is applied in the design section to set the optimum tolerance for each
design parameter to realize the designed performance, which is evaluated by the total variance of
the output of product. Tolerances of design parameters mean maximum allowable errors around the
nominal value in manufacturing process and they are closely related to the cost of manufacturing.
The nominal values of design parameters can be identified by Robust Parameter Design (RPD) through
robustness. Selection of a robust designed system by setting the optimum values of design parameters
in RPD is highly recommended prior to RTD. RPD can optimize the objective system by choosing the
optimum combination of design parameters’ nominal values from the point of view of the variability of
the output without cost-up.There is a case where RPD cannot achieve a target variability. RTD is applied, in this case, to find out
possible tolerances for realizing the target variability even with cost-up. Smaller tolerance can achieve
the smaller variability, but it means grade-up of parts or elements of the product and leads to cost-up of
manufacturing. RTD investigates the balance of quality and cost of improvement.Even when RPD achieves the target variance, RTD is applied, in some cases, to find out larger tolerance
than that considered in RPD. Larger tolerance means larger variability. However, if the increased
variability satisfies the target variability, the larger tolerance can be applicable, and it leads to cost-
down of the designing product.Purpose of RTD is to realize the target variability by setting optimum tolerance form the viewpoint
of robustness, performance and cost. For this purpose, RTD forecasts the total variance of the output
of the designing system when a tolerance of design parameter is changed. If a design parameter has
a linear effect to the output of the system, total variance of the output can be estimated based on the
result of analysis of variance (ANOVA).Assume that a design parameter F has a linear effect on the output of the system y as shown in Figure 1
(a). When the present tolerance of x in F is Δ=Δ, the error distribution of the factor F has an influence
on output y with the magnitude of σ =βΔ. When the tolerance of F is reduced to new tolerance Δ=λΔ
(λ<1 in Figure 1 (a)) , the influence of F on the output is reduced to λσ=βλΔ and the variance of y due to
the factor F is reduced from the present variance V to new variance V =λ V . As a result of this, the
FP FN FPtotal variance of the output is reduced from V to V (Figure 1 (b)).
TP TN
2 © ISO 2019 – All rights reserved
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ISO/DIS 16337:2019(E)
(a)Linear dependence of factor F (b)Total variances by tolerance change
Figure 1 — RTD mechanism for tolerance change of factor F
New total variance V can be estimated as follows;
VV=+VV=+λ V
TN FN eFPe
where λ= is assumed.
When a tolerance of design parameter is reduced, that is, λ≤1, the magnitude of error of the design
parameter becomes smaller and the total variance of output is reduced. Smaller tolerance means that
up-graded part or element will be used, and production cost of a new design may be larger than the
present design.When a tolerance of design parameter is enlarged, that is, λ≥1, the magnitude of error of the design
parameter becomes larger and the total variance of output is enlarged. Larger tolerance means that
down-graded part or element can be used, and production cost of a new design may be smaller than the
present design.RTD has the following two steps;
1) RTD experiment: Data collection of the designing system and analysis of the data to find out the
dependence of the output of the system on the design parameters.2) Tolerance determination: Forecasting the total variance when tolerance is changed, and cost
comparison for deciding the optimum tolerance.RTD experiment studies actual variability of the designing system which has some errors in design
parameters of the product. In RTD experiment, experimental design is applied to collect the data of
output of the system under the situation where errors of design parameters exist. ANOVA shows the
effects of errors in design parameters to the total variance of the output of the system. The output of
the system has a target variance from the point of view of robustness and performance.
Controllable design parameters are taken as noise factors in RTD experiment. “Controllable” means
that designer can set the nominal values and the tolerances of them. The linear effects of errors in
controllable design parameters will be estimated. The level width d of the factors is taken proportional
to tolerances. In RPD, controllable design parameters are taken as control factors because the values of
design parameters can be fixed by designer as nominal values. However, in the actual manufacturing,
the parts or elements of product have some errors and the errors of design parameters could not be
fixed by designer. Designer can fix the limit of error as a tolerance. The errors of design parameters are
causes of variability of output of the products. If an error of a factor has linear effect, the variance of
© ISO 2019 – All rights reserved 3---------------------- Page: 8 ----------------------
ISO/DIS 16337:2019(E)
output can be changed by resetting the tolerance of the design parameter. RTD experiment is applied to
find out the contribution of the linear effects of errors to the total variance of product’s output.
In tolerance determination step of RTD, the optimum tolerance can be chosen by considering the quality
merit of tolerance change expressed by quality loss and the cost of tolerance change.
4.2 RTD experiment4.2.1 Objective system
RTD experiment is applied to find the design parameters’ linear effects for the present designed system.
For this purpose, the relation between the output of the system and the error in design parameter is
investigated. Multi-factor experimental design, orthogonal array, is applied to data collection.
There are three cases of objective system for data collection;1) by a theoretical formula,
2) by an experiment with an actual system,
3) by a simulation experiment.
When theoretical formula of the objective system is known between the output and the design
parameters, the data of the output can be directly calculated by the levels of design parameters. RTD
offers orthogonal array as an experimental design for collecting the data under variation of noise
factors as shown in the case study (1) in 6.1, and ANOVA for analysing the dependence of the output on
noise factors. Mathematical analysis may be applied in this case. This mathematical analysis consists of
using variance estimates for a system, for example, by propagating input variance through the system
[4]via Taylor series expansions of moment generating functions .
When actual systems can be constructed, an actual experiment on them can be applied, and the data
of output of them can be collected. However, in many cases, it is difficult to set levels of experimental
factor in an actual system, because the levels of noise factors are set within the error distribution of
the design parameters. Simulation experiment can be applied in those cases. This is the reason why
simulation experiments are often applied in RTD. Simulation program can give the data of the output of
the objective system as shown in the case study (2) in 6.2.4.2.2 Experimental design
RTD experiment is applied for collecting the data of output of the designed system under the situation
where errors in design parameters exist. The purpose of RTD experiment is to know the linear effects
of the errors in design parameters. Orthogonal array is applied for collecting the data. Orthogonal array
with multi factor situation is effective for RTD experiment because output data under various situation
can be collected in multifactor layout.Orthogonal array L is applied for experimental layout for the factors A-H. Number of levels should be
three for seven factors and two for one factor. If the proportional property is obvious for a factor, two-
level setting is enough for this factor. Table 1 shows the factors assignment to orthogonal array L and
the output data y calculated under the combinations of factors’ levels which are indicated in low No. i of
the orthogonal array L .Table 1 — Factors assignment to orthogonal array L and the data of output
Factors A B C D E F G H Data
No. 1 2 3 4 5 6 7 8 Output
1 1 1 1 1 1 1 1 1 y
2 1 1 2 2 2 2 2 2 y
3 1 1 3 3 3 3 3 3 y
4 © ISO 2019 – All rights reserved
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ISO/DIS 16337:2019(E)
Table 1 (continued)
Factors A B C D E F G H Data
No. 1 2 3 4 5 6 7 8 Output
4 1 2 1 1 2 2 3 3 y
5 1 2 2 2 3 3 1 1 y
6 1 2 3 3 1 1 2 2 y
7 1 3 1 2 1 3 2 3 y
8 1 3 2 3 2 1 3 1 y
9 1 3 3 1 3 2 1 2 y
10 2 1 1 3 3 2 2 1 y
11 2 1 2 1 1 3 3 2 y
12 2 1 3 2 2 1 1 3 y
13 2 2 1 2 3 1 3 2 y
14 2 2 2 3 1 2 1 3 y
15 2 2 3 1 2 3 2 1 y
16 2 3 1 3 2 3 1 2 y
17 2 3 2 1 3 1 2 3 y
18 2 3 3 2 1 2 3 1 y
Table 2 shows an example of factors’ levels of design parameters for the orthogonal array L . Upper
and lower tolerances are assumed to be same for simplicity. Levels of experimental noise factors are set
around the nominal value m with the level width d. Nominal value m is set as an optimum value by RPD
from the point of view of robustness.Table 2 — Example of level settings of factors
Factor 1 2 3
A m -d m +d -
A A A A
B m -d m m +d
B B B B B
C m -d m m +d
C C C C C
D m -d m m +d
D D D D D
E m -d m m +d
E E E E E
F m -d m m +d
F F F F F
G m -d m m +d
G G G G G
H m -d m m +d
H H H H H
When actual standard deviation σ of the error in design parameter is not exactly known, assumptions
Δ Δσ = or σ = may be applied.
x x
2 3
When actual standard deviation σ of the error in design parameter is known, the level width d and
levels of the factors are set as follows;For two-level factor, d=σ :
X1: First level xm=−σ
1 x
X2: Second level xm=+σ
2 x
For three-level factors, d= σ :
© ISO 2019 – All rights reserved 5
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ISO/DIS 16337:2019(E)
X1: First level xm=−dm=− σ
1 x
X2: Second level xm=
X3: Third level xm=+dm=+ σ
3 x
By setting the level of noise factors as mentioned above, the variance σ of the output y caused by the
linear effect of the error in noise factor becomes βσ . where β represents a linear coefficient of the
relation yx=β between output y and input x.Assume that data yi()==11,,nj,, ,r are taken as r repeated data on i level of x , linear coefficient
ij iβ and sum of squares of a liner effect S are calculated as follows;
n r
()xx−−()yy
iij
i=1 j=1
β= ,
rx()−x
i=1
n r
()xx−−()yy
iij
i=1 j=1
2 2
S = =−rx()x ⋅β .
β i
i==1
rx()−x
i=1
For two-level factor A with the levels of xx=−d and xx=+d , the sum of squares of a liner effect S
1 2 βis calculated as Sr=⋅2d β . If the linear effect of the factor A is significant, S approximately
β β2 2
represents data number times of variance σ of each data, that is, 2rσ . If the level width d is set as
y y22 22 2 2
σ , Sr==22drβσ βσ≅2r . Then the variance σ of the output y caused by the linear effect of
x β xy ythe error in noise factor becomes βσ .
For three-level factor B with the levels of xx=−dx, =x , and xx=+d , the sum of squares of a liner
12 3effect S is calculated as Sr=⋅2d β . If the linear effect of the factor is significant, S approximately
β β β2 2
represents data number times of variance σ of each data, that is, 3rσ . If the level width d is set as
y y22 22 22 2
σ , Sr==22drβσ⋅⋅ββ=≅33rrσσ . Then the variance σ of the output y caused by the
x β xx y y
linear effect of the error in noise factor becomes βσ .
4.2.3 Analysis of variance of data of RTD experiment
Analysis of Variance (ANOVA) is applied to find out the linear effects of the factors and their contribution
ratios to the total variance.6 © ISO 2019 – All rights reserved
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ISO/DIS 16337:2019(E)
Calculations of ANOVA for orthogonal array L are as follows;
Total sum of squares:
()y
∑ i
18 18
i=1
2 2
Sy=−()yy=−
T i i
i==1 i 1
Total sum of squares is decomposed to sum of squares S of linear effect of each factor and sum of
squares S of error as follows;SS=+SS++SS++SS++SS+
TeABCDEF GH
For calculating factors’ effects, sum of data of each level of factors are calculated;
Yy=+yy++yy++yy++yy+A1 12 34 56 789
Yy=+y +++yyy ++y yyyy++
A2 10 11 12 13 14 15 16 17 18
Yy=+yy+ +++yy y
B1 1 23101112
Yy=+yy++yy++y
B2 45 61314 115
Yy=++yy +++yyy
B3 789 16 17 18
Yy=+yy++yy++y
H3 3 47121417
Table 3 shows the summary of calculated sum of data of each levels of factors.
Table 3 — Sum of data for each level of factors
Factors Sum of data
Level 1 Level 2 Level 3
A Y Y -
A1 A2
B Y Y Y
B1 B2 B3
C Y Y Y
C1 C2 C3
D Y Y Y
D1 D2 D3
E Y Y Y
E1 E2 E3
F Y Y Y
F1 F2 F3
G Y Y Y
G1 G2 G3
H Y Y Y
H1 H2 H3
For two-level factor (A):
2 2 2 2
YY+ ()YY+ ()YY−
AA1 2 AA12 AA12
S = − =
918182×
For three-level factor (factor B, for example):
Effect of each three-level factor is separated into two parts; a linear term and a quadratic term.
© ISO 2019 – All rights reserved 7---------------------- Page: 12 ----------------------
ISO/DIS 16337:2019(E)
Total effect of factor B:
2 2 2
YY++Y
YY++Y ()
BB12 B3
BB1 2 B3
S = −
618
Linear term of factor B:
2 2
()−∗10YY+∗ +∗1 YY ()−∗10+∗YYY+∗1
BB132B B1 B2 B3
S = =
22 2
62×
61×−() ++01
Quadratic term of factor B:
2 2
12∗+YY()−∗ +∗1 YY12∗+()−∗YYY+∗1
BB132B B1 B2 B3
S = =
22 2
66×
61×+()−+21
Following relation is useful for checking the calculations;
SS=+S .
BB Bq
Calculations of factor’s effect are applied to all other 3-level factors, factors C to H.
Result of ANOVA calculations is shown in Table 4.Table 4 — Result of ANOVA calculations
f SS V
A 1 S V
A A
Bl 1 S V
Bl Bl
Bq 1 S V
Br Br
Cl 1 S V
Cl Cl
Cq 1 S V
Cr Cr
Dl 1 S V
Dl Dl
Dq 1 S V
Dr Dr
El 1 S V
El El
Eq 1 S V
Er Er
Fl 1 S V
Fl Fl
Fq 1 S V
Fr Fr
Gl 1 S V
Gl Gl
Gq 1 S V
Gr Gr
Hl 1 S V
Hl Hl
Hq 1 S V
Hr Hr
e 2 S V
e e
T 17 S
If linear effect of a factor is smaller than the error effect, it is pooled to the error effect.
If quadratic effect of a factor is small compared with a linear effect and it is comparable to the error
effect, it is pooled to the error effect.If quadratic ef
...
FINAL
INTERNATIONAL ISO/FDIS
DRAFT
STANDARD 16337
ISO/TC 69/SC 8
Application of statistical and related
Secretariat: JISC
methods to new technology and
Voting begins on:
20210203 product development process —
Robust tolerance design (RTD)
Voting terminates on:
202103-31
Application des méthodes statistiques et des méthodes liées aux
nouvelles technologies et de développement de produit — Plans
d'expériences robustes
RECIPIENTS OF THIS DRAFT ARE INVITED TO
SUBMIT, WITH THEIR COMMENTS, NOTIFICATION
OF ANY RELEVANT PATENT RIGHTS OF WHICH
THEY ARE AWARE AND TO PROVIDE SUPPOR TING
DOCUMENTATION.
IN ADDITION TO THEIR EVALUATION AS
Reference number
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO
ISO/FDIS 16337:2021(E)
LOGICAL, COMMERCIAL AND USER PURPOSES,
DRAFT INTERNATIONAL STANDARDS MAY ON
OCCASION HAVE TO BE CONSIDERED IN THE
LIGHT OF THEIR POTENTIAL TO BECOME STAN
DARDS TO WHICH REFERENCE MAY BE MADE IN
NATIONAL REGULATIONS. ISO 2021
---------------------- Page: 1 ----------------------
ISO/FDIS 16337:2021(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2021
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting
on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address
below or ISO’s member body in the country of the requester.ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2021 – All rights reserved
---------------------- Page: 2 ----------------------
ISO/FDIS 16337:2021(E)
Contents Page
Foreword ........................................................................................................................................................................................................................................iv
Introduction ..................................................................................................................................................................................................................................v
1 Scope ................................................................................................................................................................................................................................. 1
2 Normative references ...................................................................................................................................................................................... 1
3 Terms and definitions ..................................................................................................................................................................................... 1
4 Robust tolerance design ............................................................................................................................................................................... 2
4.1 General ........................................................................................................................................................................................................... 2
4.2 RTD experimentation ........................................................................................................................................................................ 4
4.2.1 Data generation ...................................................................... ........................................................................................... 4
4.2.2 Experimental design for data collection ...................................................................................................... 4
4.2.3 Analysis of variance ....................................................................................................................................................... 7
4.3 Tolerance determination .............................................................................................................................................................10
4.3.1 Estimating total variance if tolerance is changed .............................................................................10
4.3.2 Deciding tolerance .......................................................................................................................................................11
5 RTD case study (1) — Stabilizing a circuit by using theoretical formula ...............................................12
5.1 Experimentation .................................................................................................................................................................................12
5.1.1 Objective ...................................................................... .........................................................................................................12
5.1.2 Experimental design for data collection and analysis of variance .....................................13
5.2 Tolerance determination .............................................................................................................................................................16
6 RTD case study (2) — Stabilizing the piston by using a simulation experiment ............................18
6.1 Experimentation .................................................................................................................................................................................18
6.1.1 Objective ...................................................................... .........................................................................................................18
6.1.2 Experimental design for data collection and analysis of variance .....................................18
6.2 Tolerance determination .............................................................................................................................................................21
Bibliography .............................................................................................................................................................................................................................26
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ISO/FDIS 16337:2021(E)
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
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and nongovernmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.The procedures used to develop this document and those intended for its further maintenance are
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
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/ patents).Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see URL: www
.iso .org/ iso/ foreword .html.This document was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 8, Application of statistical and related methodology for new technology and product
development.Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/ members .html.iv © ISO 2021 – All rights reserved
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ISO/FDIS 16337:2021(E)
Introduction
The designer of a product typically decides the specifications of the product and passes them on to the
manufacturing section for use in manufacturing the product. The specifications include the designed
nominal values and tolerances for the parts and/or elements of the product. The optimum nominal
values of the design parameters are determined by robust parameter design (RPD), and the optimum
tolerances are determined by robust tolerance design (RTD).RPD, as described in ISO 16336, is applied to the product prior to RTD. In RPD, the major noise factors are
used to evaluate robustness as measured by the signal-to-noise ratio, which represents the variability
of product output. It is a measure for comparing robustness between levels of control factors. RPD
identifies the combination of the values of the design parameters as an optimum RPD condition for
minimizing the variability, that is, maximizing the robustness.RTD, as described in this document, is a method for selecting the degree of errors of the parts or
elements of the product from the viewpoint of variability under the optimum RPD condition, that is,
the combination of optimum nominal values of the design parameters. If a manufactured product has
errors from the designed nominal values, the product output will deviate from the designed value. The
error in a design parameter should be smaller than the designed error limit to keep the product output
within the designed variability. This is why the design parameters need a tolerance.
The design of a product can be finalized by setting the optimum error limits of the design parameters
by using RTD. The expected variance in output of a product manufactured with errored parts or
elements can be estimated using RTD. After RPD is used to identify a set of optimum values for the
design parameters, RTD is used to check whether the estimated variance is smaller than the target
variance under the optimum RPD condition.RPD can be used to set the optimum nominal values of the design parameters without increasing
manufacturing cost while RTD is closely related to the manufacturing cost. Smaller tolerances, meaning
highergrade parts or elements, result in higher costs, while larger tolerances, meaning lowergrade
parts or elements, result in lower costs. To finalize the product design, the cost of manufacturing the
product is considered. The loss function in the Taguchi methods is used to transform the benefits of an
improvement in quality into a monetary amount, the same as a cost.The cost of the improvement and the benefits of the improvement in quality should be balanced in
deciding the tolerances. RPD and RTD together provide a cost-effective way of optimizing product design.
If RPD cannot achieve the product variability smaller than the target variability, the tolerances of the
design parameters are reduced to improve the variability, but smaller tolerances result in higher costs.
On the other hand, if RPD can achieve the product variability much smaller than the target variability,
the tolerances of the design parameters are increased to reduce manufacturing cost, so larger tolerances
result in lower costs.Products manufactured with optimum nominal values and tolerances of design parameters are robust
to noise situations under usage conditions after shipment. Robust products minimize users’ quality
losses due to defects, failures, and quality problems.© ISO 2021 – All rights reserved v
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FINAL DRAFT INTERNATIONAL STANDARD ISO/FDIS 16337:2021(E)
Application of statistical and related methods to new
technology and product development process — Robust
tolerance design (RTD)
1 Scope
This document specifies guidelines for applying the robust tolerance design (RTD) provided by the
Taguchi methods to a product in order to finalize the design of the product.NOTE 1 RTD is applied to the target product to set the optimum tolerances of the design parameters around
the nominal values. RTD identifies the effects of errors in the controllable design parameters on product output
and estimates the total variance of the product output if the tolerances are changed. Hence, RTD achieves the
target variance of the output from the viewpoints of robustness, performance, and cost.
NOTE 2 The tolerance expresses a maximum allowable error in the value of a design parameter in the
manufacturing process. In a perfect world, the parts or elements of every product have the designed nominal
values of the design parameters. However, actual manufacturing does not reproduce the exact designed nominal
values of the design parameters for all products. The actual products have errors in the values of their parts or
elements. These errors are supposed to be within the designed tolerances.2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 16336, Applications of statistical and related methods to new technology and product development
process — Robust parameter design (RPD)3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 16336 apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp— IEC Electropedia: available at http:// www .electropedia .org/
3.1
tolerance
difference between the upper specification limits and lower specification limits
3.2
robust tolerance design
RTD
method of setting optimum tolerances from the viewpoints of robustness, performance, and cost
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ISO/FDIS 16337:2021(E)
4 Robust tolerance design
4.1 General
A company’s product design section normally gives the specifications of a product, that is, the nominal
values and tolerances of the design parameters, to the manufacturing section. The manufacturing
section uses the designed specifications in manufacturing the product. When specifications specify the
limits of a design parameter as m±Δ , the parameter value x in the manufacturing process should
satisfy the following restriction:mx−≤ΔΔ≤+m , (1)
where m and Δ denote a nominal value and its permissible difference, respectively. Only the symmetric
(±Δ ) case is discussed in this document. In the symmetric case, the tolerance is 2Δ, and the permissible
difference Δ is half the tolerance.If the absolute error of a design parameter is larger than the specified permissible difference Δ, the
variability in the product output cannot meet the designed performance and specifications.
RTD is used by the design section to set the optimum tolerance for each design parameter to achieve
the designed performance, which is evaluated based on the total variance of the product output. The
permissible difference of a design parameter is the maximum allowable error around the nominal value
in the manufacturing process, and it is closely related to the cost of manufacturing.
The optimum nominal values of the design parameters can be identified by robust parameter design
[1](RPD) through robustness measure, signaltonoise ratio . The selection of a robust product by setting
the nominal values as the optimum values using RPD prior to RTD is highly recommended. RPD can
optimize the target product by choosing the optimum combination of design parameter nominal values
[2]from the viewpoint of the variability of the product output without increasing the cost .
If RPD cannot achieve a target variability, RTD is used to identify possible tolerances for achieving the
target variability even at a higher cost. Smaller tolerances result in smaller variability, but this requires
upgrading the parts or elements of the product, which leads to higher manufacturing cost. RTD is used
to investigate the balance between product quality and improvement cost.Even if RPD achieves the target variance, RTD is used, in some cases, to identify larger tolerances than
those considered in RPD. Larger tolerances mean larger variability, but if the increased variability
satisfies the target variability, the larger tolerances are applicable as they lead to reduced cost of
manufacturing the designed product.The purpose of RTD is to achieve the target variability by setting optimum tolerances from the
viewpoints of robustness, performance, and cost. For this purpose, RTD estimates the total variance of
the output of the designed product if the tolerance of a design parameter is changed. The total variance
can be estimated based on the results of analysis of variance (ANOVA).Assume that a value x of design parameter F has a linear effect on output y of the product, as shown in
Figure 1 a). If the present permissible difference of x in F is Δ = Δ, the error distribution of F affects
output y with a magnitude of βΔ. If the permissible difference Δ of F is reduced to new permissible
difference Δ = λΔ [λ<1 in Figure 1 a)], the effect of changing Δ in F on the output is reduced to λβΔ,
and the variance in y due to changing Δ in F is reduced from the present variance V to new variance
V = λ V . As a result, the total output variance is reduced from V to V [Figure 1 b)].
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ISO/FDIS 16337:2021(E)
a) Linear dependence on x in F b) Change in total variance
Figure 1 — Effect of changing Δ in design parameter F on total variance
The new total variance V can be estimated as
VV=+VV=+λ V , (2)
TN FN eFPe
where λ= is assumed.
If the tolerance of a design parameter is reduced, that is, λ<1, the magnitude of error of the design
parameter becomes smaller, and the total output variance is reduced. A smaller tolerance means that
an upgraded part or element is used, so the cost of producing the new design can be higher than that of
the present design.If the tolerance of a design parameter is enlarged, that is, λ>1, the magnitude of error of the design
parameter becomes larger, and the total output variance is enlarged. A larger tolerance means that a
downgraded part or element is be used, so the cost of producing the new design can be smaller than
that of the present design.RTD comprises two steps, as follows.
1) RTD experimentation: Collect data on the designed product, and analyse the data to determine the
dependence of the product output on the design parameters.2) Tolerance determination: Estimate the total variance if a tolerance is changed, and compare the
effects in quality with the cost of the change to identify the optimum tolerance.
RTD experiments collect the output data of the designed product in which there are errors in the product
design parameters, and estimate the total variance and its dependence on the design parameters. The
experimental design plan is used to collect the data under the combination of design parameter errors.
The ANOVA results show the effects of errors in the design parameters on the product output. The
product output has a target variance from the viewpoints of robustness and performance.
In RTD experiments, the design parameters are taken as noise factors. A noise factor is an experimental
factor which is taken into experiment for the purpose of estimating its variability. The variance in the
linear effect of errors in the design parameters is estimated.In RPD, on the other hand, the design parameters are taken as control factors. A control factor is an
experimental factor which is taken into experiment for the purpose of selecting the optimum level of the
factor. Designers can fix the nominal values of design parameters to the optimum RPD values. However,
in actual manufacturing, the parts or elements of the product invariably have errors, so the designer
cannot specify the error of a design parameter. The designer can set only the permissible difference Δ
as an error limit.© ISO 2021 – All rights reserved 3
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ISO/FDIS 16337:2021(E)
Design parameter errors cause variability in product output. If the error of a design parameter has a
linear effect on the product output, the output variance can be changed by resetting the tolerance of the
design parameter. RTD experimentation is used to determine the contributions of the effects of errors
in design parameters to the product output.In the tolerance determination step of RTD, the change in the output variance due to resetting a
tolerance is estimated, and the designer selects optimum tolerance for achieving the target output
variance. The optimum tolerance can be determined by balancing the effect in quality due to a tolerance
[3]change against the cost of the tolerance change .
4.2 RTD experimentation
4.2.1 Data generation
RTD experimentation is used to determine the design parameters’ linear effects for the designed
product. The relationship between the output by the product and the errors in the design parameters is
investigated. The output data can be generated in three ways:1) by using a theoretical formula,
2) by experimentation with an actual product;
3) by simulation experimentation.
When the theoretical relationship between the product output and the design parameters is known,
the output data can be directly calculated for various combination of the design parameter values.
RTD offers multi-factor design as an experimental design for generating the output data in various
combinations of the level of experimental factors, as shown in case study (1) in Clause 5. ANOVA is used
for analysing the dependence of the product output on the factors.Mathematical analysis can be applied in this case. Mathematical analysis consists of using variance
estimates for a system by, for example, propagating an input variance through the system via Taylor
[4]series expansions of moment generating functions .
If an actual product can be constructed, it can be used for experimentation, and the data output can be
collected using the actual experiment. However, in many cases, it is difficult to set the intended levels
of the errors of design parameters in an actual product because the noise levels cannot be controlled
within the error distribution of the design parameters. Simulation experimentation can be used in such
cases. This is why simulation experiments are often used in RTD. A simulation program can provide the
product output data, as shown in case study (2) in Clause 6.4.2.2 Experimental design for data collection
RTD experimentation is used for collecting output data for the designed product under the combinations
of design parameter errors. There are many design parameters, and a multi-factor experimental design
is used to generate various such combinations. The purpose of RTD experimentation is to determine
the main effects of experimental factors. An orthogonal array plan is recommended as a multi-factor
experimental plan for collecting the data as it is an efficient way to collect data for an RTD experiment.
An orthogonal array plan can reduce the number of experimental runs compared with a full-factorial
plan for the same number of factors and can assign the maximum number of factors in a plan for the
same number of experimental runs. The main effects of factors can be estimated under the condition of
a balanced combination of the other factors’ levels. The choice of the orthogonal array depends on the
[3]numbers of factors and their levels .
An example orthogonal array (L ) is shown in Table 1. Seven experimental factors with three levels
(B-H) and one factor with two levels (A) can be assigned to the columns in the array. Rows represent
the experimental run. The number in each cell represents the level of the factor assigned to the column.
The experimental run of low No. 1 should be performed under the combination of factor’s levels
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ISO/FDIS 16337:2021(E)
For RTD, the design parameters are assigned to the columns as noise factors. For the purpose of
estimating the linear and nonlinear effects of a factor, each factor has at least three levels. However,
if the proportional property is obvious for a factor, a two-level setting is sufficient. Two-level factor
is assigned to the first column. The last column in Table 1 shows the output data y calculated for the
combination of factors’ levels shown in the cells in the same lowTable 1 — Example of orthogonal array L and output data
Column 1 2 3 4 5 6 7 8 Data
output
A B C D E F G H
No.
1 1 1 1 1 1 1 1 1 y
2 1 1 2 2 2 2 2 2 y
3 1 1 3 3 3 3 3 3 y
4 1 2 1 1 2 2 3 3 y
5 1 2 2 2 3 3 1 1 y
6 1 2 3 3 1 1 2 2 y
7 1 3 1 2 1 3 2 3 y
8 1 3 2 3 2 1 3 1 y
9 1 3 3 1 3 2 1 2 y
10 2 1 1 3 3 2 2 1 y
11 2 1 2 1 1 3 3 2 y
12 2 1 3 2 2 1 1 3 y
13 2 2 1 2 3 1 3 2 y
14 2 2 2 3 1 2 1 3 y
15 2 2 3 1 2 3 2 1 y
16 2 3 1 3 2 3 1 2 y
17 2 3 2 1 3 1 2 3 y
18 2 3 3 2 1 2 3 1 y
Table 2 shows an example of level setting of factors for RTD. The upper and lower permissible differences
are assumed to be the same for simplicity. The levels of the factors are set around nominal value m with
level width d. Nominal value m is set to an optimum value by RPD from the viewpoint of robustness.
Level width d is set from the actual standard deviation of the design parameter if it is known.
Table 2 — Example of level settings of factors for RTDFactor 1 2 3
A m − d m + d —
A A A A
B m − d m m + d
B B B B B
C m − d m m + d
C C C C C
D m − d m m + d
D D D D D
E m − d m m + d
E E E E E
F m − d m m + d
F F F F F
G m − d m m + d
G G G G G
H m − d m m + d
H H H H H
When the actual standard deviation σ of the error in the design parameter is not exactly known, the
Δ Δassumption σ = or σ = can be applied.
x x
2 3
When the actual standard deviation σ of the error in the design parameter is known, the level width d
and the levels of the factors are set as follows.© ISO 2021 – All rights reserved 5
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ISO/FDIS 16337:2021(E)
For a twolevel factor, d=σ :
X1: First level xm=−σ , (3)
1 x
X2: Second level xm=+σ . (4)
2 x
For a threelevel factor, d= σ :
X1: First level xm=−dm=− σ , (5)
1 x
X2: Second level xm= , (6)
X3: Third level xm=+dm=+ σ . (7)
3 x
Setting the level of the factors in this way makes the estimated variance σ of output y caused by the
linear effect of the error in the factor βσ , where β represents the linear coefficient of the relationship
yx=β between output y and input x.If yi==11,,nj,, ,r represents the output from jth run in r repeated runs on ith level x in n
ij ilevel factor, the linear coefficient β and the sum of squares of linear effect S are calculated as
n r()xx−−()yy
iij
i=1 j=1
β= , (8)
rx()−x
i=1
n r
()xx−−()yy
iij
i=1 j=1
2 2
S = =−rx()x ⋅β . (9)
β i
i==1
rx()−x
i=1
For a twolevel factor A with levels xx=−d and xx=+d , the sum of squares of linear effect S is
1 2 βcalculated as Sr=⋅2d β . If the linear effect of factor A is significant, S approximately represents
β β2 2
2rσ , where 2r denotes the number of data items and σ denotes the variance of each. If level width
y y22 22 2 2
d is set to σ , Sr==22drβσ βσ≅2r . Then variance σ in output y caused by the linear effect
x β xy y22 2
of the error in the factor becomes σβ= σ .
yx
For a threelevel factor B with levels xx=−dx, =x , and xx=+d , the sum of squares of linear effect
12 3S is calculated as Sr=⋅2d β . If the linear effect of the factor is significant, S approximately
β β β2 3
represents 3rσ , where 3r denotes the number of data items. If the level width d is set to σ ,
y x22 22 22 2 2
Sr==22drβσ⋅⋅βσ=≅33rrβσ . Then variance σ in output y caused by the linear effect of
β xx y y22 2
the error in the noise factor becomes σβ= σ .
yx
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ISO/FDIS 16337:2021(E)
4.2.3 Analysis of variance
ANOVA is used to identify the linear effects of the factors and the ratios of their contributions to the
total variance.The ANOVA calculations for orthogonal array L are as follows.
Total sum of squares:
()y
18 18
i=1
2 2
Sy=−()yy=− . (10)
T i i
i==1 i 1
The total sum of squares is decomposed into sum of squares S of the linear effect of each factor and
sum of squares S of the error as follows:...
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