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Traditionally, tolerances are defined by an interval [LSL; USL] which can lead to several ambiguous interpretations of conformity. This paper examines an alternative method for setting specifications: “inertial tolerancing”. Inertial tolerancing consists of tolerancing the mean square deviation from the target rather than the distance. This alternative has numerous advantages over the traditional approach, particularly in the case of product assembly, mixed batches and conformity analysis. Coupled with a capability index Cpi, this alternative method leads to minimizing production costs for a specified level of quality. We propose to compare both approaches: traditional and inertial tolerancing.
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Research and concepts
Inertial tolerancing
Maurice Pillet
The author
Maurice Pillet is a Professor in the Department of Industrial
Engineering at the Universite
´
de Savoie, Annecy le Vieux, France.
Keywords
Taguchi methods, Statistical tolerance levels, Production costs
Abstract
Traditionally, tolerances are defined by an interval [LSL; USL]
which can lead to several ambiguous interpretations of
conformity. This paper examines an alternative method for
setting specifications: “inertial tolerancing”. Inertial tolerancing
consists of tolerancing the mean square deviation from the
target rather than the distance. This alternative has numerous
advantages over the traditional approach, particularly in the case
of product assembly, mixed batches and conformity analysis.
Coupled with a capability index Cpi, this alternative method
leads to minimizing production costs for a specified level of
quality. We propose to compare both approaches: traditional and
inertial tolerancing.
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1. Main tolerancing methods in the case of
assembled products
1.1 Conformity and tolerancing
In the case of assembled products or, more
generally, in the case where a functional
characteristic is the result of a linear combination
of several elementary characteristics, we have the
problem of tolerancing the elementary
characteristics. With no variation in production, it
would be useless to determine tolerances and
define the target. The purpose of tolerancing is to
help maximize organizational profitability by
minimizing the total cost of assembly, test, and
design while simultaneously maximizing product
quality and reliability. Minimizing the total cost of
assembly leads to increasing the tolerance whilst
maximizing product quality, which leads to a
reduction in the tolerances. Tolerancing consists in
obtaining the interval that will give the best
compromise economically. Many studies have
been carried out on this subject and was
standardized (ANSI, 1982; ASME, 1994a, b; ISO
286, 1988; ISO 5458, 1998).
Tolerancing is linked to conformity. The quality
of the product is judged in terms of whether it
meets specification or design requirements. Failure
of a specific characteristic to meet the specification
represents a defect or non-conformance. However,
if all production is very close to the limit, it will
have serious problems in assembly. It is generally
viewed that the conformity is accepted when the
products are included in the bi-point [USL; LSL].
Several capability indexes are founded on this
definition as Cpk (Ford, 1991). The capability
index Cpm (Chan et al., 1988) is based on another
definition, the Taguchi’s loss function (Taguchi,
1987).
In the case of assembled products with the
traditional bi-point, one must share the final
functional condition Y of all elementary
characteristics X
i
. Several approaches were
proposed. Let us remind ourselves of the main
results in the case of a linear relationship between
Y and x
i
(Chase and Prakinson, 1991; Grant,
1946; Graves, 1997, 2001; Graves and Bisgaard,
2000; Shewhart, 1931):
Y ¼
a
0
þ
X
n
i ¼1
a
i
x
i
ð1Þ
1.2 Worst case tolerancing
In this case, one considers that the final condition
Y will be respected in all cases of assembling. In
worst case tolerancing, the elementary tolerances
are calculated by the equations:
t
y
¼
X
a
i
t
xi
ð2Þ
The TQM Magazine
Volume 16 · Number 3 · 2004 · pp. 202-209
q Emerald Group Publishing Limited · ISSN 0954-478X
DOI 10.1108/09544780410532918
202
D
y
¼
X
j
a
i
jD
xi
ð3Þ
Notation:
t
y
: Y
target
D
Y
: USL[Y ]2 LSL[Y ]
The tolerance sharing can be carried out using
different methods (Graves, 2001):
.
uniform tolerances sharing;
.
consideration of standard or design rules;
.
proportional to the square root of the nominal
dimension; and
.
consideration of the capability experience.
The well known disadvantage of worst case
tolerancing is the high cost associated with this
method. Indeed, it leads to very tight tolerances
which are very difficult to obtain in production.
Consequently, the cost of inspection, rejects and
reworking increases as does the choice of a more
sophisticated product method. The main
advantage is the guarantee of the specification at
the final level of assembly.
1.3 Statistical tolerancing
Statistical tolerancing was developed in order to
consider the low probability of having several
characteristics in limit of tolerance at the same
time (Evans, 1975; Shewhart, 1931). From
equation (1), in the case where the variables x
i
are
independent of a standard deviation
s
i
, one has the
relationship:
s
Y
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
a
2
i
s
2
i
q
ð4Þ
With tolerances proportional to the standard
deviation, we obtain (Chase and Prakinson, 1991)
the equation:
T
Y
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
n
i¼1
a
2
i
T
2
i
s
ð5Þ
In this tolerancing method, the basic assumption is
the centering of all the elementary characteristics
on the target.
1.4 Inflated statistical tolerancing
Several methods were proposed in order to thwart
the negative aspects of statistical tolerancing. The
main one is inflated statistical tolerancing (Graves,
1997, 2001; Graves and Bisgaard, 2000). The
tolerance is defined by the relationship:
T
Y
¼ f
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
n
i ¼1
a
2
i
T
2
i
s
ð6Þ
where f represents the inflated coefficient. We often
choose this coefficient arbitrarily around 1.5. In
the case where the
a
i
coefficients are equal, f ¼ 1is
the statistical tolerancing and f ¼
ffiffi
n
p
is the worst
case tolerancing. Graves and Bisgaard (2000)
discuss different situations which lead to different
choices for f. They propose an interesting
approach to optimize the f coefficient in
relationship to the capability indexes. But, despite
the great quality of the tolerancing method, it is
always possible to find a situation in which the
method will not be appropriate.
2. Inertial tolerancing
2.1 Definition
The goal of tolerancing consists in determining a
criterion of acceptance for the elementary
characteristic x
i
guaranteeing the acceptance of the
resulting characteristic Y
i
. The tolerance limits the
cost of non-quality generated by a variation
compared to this target. In the case of a good
design, when Y is placed on the target, quality is
robust compared to the operating and
environmental conditions. When Y moves away
from the target, the quality will be increasingly
sensitive to the conditions, and could lead to the
customer being dissatisfied. Taguchi (1987) has
showed that the financial loss associated (L) with a
shift to the target was proportional (coefficient K)
to the square of the variation:
L ¼ K ðY
i
2 targetÞ
2
ð7Þ
In the case of a batch with an average
m
, the
associated loss is:
L ¼ K
s
2
Y
þð
m
2 targetÞ
2

¼ K
s
2
Y
þ
d
2
Y

ð8Þ
where K is a constant, and I
Y
¼
s
2
Y
þ
d
2
Y

is the
mean square deviation (MSD) of the target. The
MSD behaves like inertia arround a point p:
I ¼ MassðI 2 pÞ
2
: In order to have the minimal
“inertia”, we must have the products as near to the
target as possible. As with inertia, the MSD has the
very interesting property of additivity in the case of
the linear relationship between Y and x
i
. To take
advantage of this property, we propose to replace
the traditional tolerance Y ^ DY by the tolerance
Y(I
Y
) in which I
Y
represents the maximum MSD
accepted on variable Y. By analogy of the MSD
with inertia, we have chosen to name this
alternative method “inertial tolerancing”. This
way of determining the tolerances has interesting
properties that we propose to develop.
2.2 An adapted capability index (Cpi)
In the case of inertial tolerancing, conformity is
declared if the inertia I
Y
of the characteristic or
the batch is lower than the fixed maximum
inertia I
YMax
. I
YMax
is a tolerance on I
Y
.Itis
Inertial tolerancing
Maurice Pillet
The TQM Magazine
Volume 16 · Number 3 · 2004 · 202-209
203
possible to define a capability indicator Cpi by the
equation:
Cpi ¼
I
Y Max
I
Y
ð9Þ
A manufacturing process must obtain Cpi higher
than 1 (I
Y
, I
YMax
). Later in this paper, we will show
that this indicator has many properties in particular,
in the case of mixed batches. The Cpi of two mixed
batches is equal to the average of both Cpi.
2.3 Extreme situations of acceptance in the
case of inertial tolerance
Let us study the extreme situations of acceptance
in the case of inertial tolerancing. Inertia can
increase under the influence of two parameters: a
shift of the average compared to the target (
d
Y
)or
an increase in spread (
s
Y
) and this independently
of the distribution form.
Centered extreme situation (
d
Y
¼ 0):
I
Y
¼
s
2
Y
þ
d
2
Y

: Then I
Y
¼
s
2
Y
ð10Þ
One thus obtains:
s
Y Max
¼
ffiffiffiffiffiffiffiffiffiffiffiffi
I
Y Max
p
ð11Þ
Extreme situation with a standard deviation equal
to zero (
s
Y
¼ 0)
I
Y
¼
d
2
Y
ð12Þ
One thus obtains:
d
Y Max
¼
ffiffiffiffiffiffiffiffiffiffiffiffi
I
Y Max
p
ð13Þ
Extreme
m
shift accepted according to the standard
deviation (Figure 1).
In the case of inertial tolerancing, accepted
extreme shift will be a function of the standard
deviation:
d
Y Max
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
I
Y Max
2
s
2
Y
q
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 2
s
2
Y
=I
Y Max
q
ffiffiffiffiffiffiffiffiffiffiffiffi
I
Y Max
p
d
=
ffiffiffiffiffiffiffiffiffiffiffiffi
I
Y Max
p
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 2
s
Y
=
ffiffiffiffiffiffiffiffiffiffiffiffi
I
Y Max
p

2
r
ð14Þ
Equation (14) is represented in Figure 1. As long
as
s
, 0:6
ffiffiffiffiffiffiffiffiffiffiffiffi
I
Y Max
p
; one can have relatively
significant shift
d
, 0:8
ffiffiffiffiffiffiffiffiffiffiffiffi
I
Y Max
p
: Similarly, as long
as the shift is low, one can accept a relatively
significant spread.
2.4 Tolerance determination in the case of a
mechanical assembly
The properties of inertial tolerancing come from
the properties of the inertia’s additivity. To
illustrate this property, we will take the case of a
resulting characteristic Y dependent on a linear
function of several independent elementary
characteristics x
i
(equation (1)).
In this case, it is easy to show that we have:
s
2
Y
¼
X
a
2
i
s
2
i
ð15Þ
d
Y
¼
X
a
i
d
i
ð16Þ
Let us calculate the inertia obtained on the
characteristic Y:
I
Y
¼
s
2
Y
þ
d
2
Y
¼
X
a
2
i
s
2
i
þ
X
a
i
d
2
i

I
Y
¼
X
a
2
i
s
2
i
þ
X
a
2
i
d
2
i
þ 2
X
a
i
a
j
d
i
d
j
which is written as:
I
Y
¼
X
a
2
i
I
X
i
þ 2
X
a
i
a
j
d
i
d
j
ð17Þ
The first part of the equation corresponds to the
additivity of different inertia. The double product
corresponds to the case where all shifts are on the
same side. In the case of random distribution of the
averages when the component count is significant,
one can consider that this double product is equal
to zero. We have a hypothesis here that is close to
the assumption of traditional statistical
tolerancing. On the other hand, in cases where the
number of components is not significant or when
the average distribution is not random, the worst
case assumption makes it possible to integrate the
double product in the distribution of inertias
(equation (18)). From equation (17), we can
calculate the distribution of inertias of each
elementary characteristic according to the inertia
desired on the resulting characteristic. This
equation makes it possible to integrate the risk of
unfavorable systematic decentring of all the
elements. This equation easily makes it possible to
determine the tolerances on the elementary
characteristics according to the following three
hypotheses.
2.4.1 Assumption 1. Worst case
Under these conditions, we saw (equation (13))
that maximum decentring was
d
Y Max
¼
ffiffiffiffiffi
I
Y
p
.
Figure 1 Limit of the
m
shift accepted according to the sigma for
an inertia
I
Y
Max
¼1
Inertial tolerancing
Maurice Pillet
The TQM Magazine
Volume 16 · Number 3 · 2004 · 202-209
204
Equation (17) becomes:
I
Y Max
¼
X
a
2
i
I
i Max
þ 2
X
a
i
a
j
ffiffiffiffiffiffiffiffiffiffi
I
i Max
p
ffiffiffiffiffiffiffiffiffiffi
I
jMax
p
ð18Þ
Equation (18) is simplified in the case where
a
i
¼
1 and in the uniform distribution of inertia
(I
iMax
¼ I
Max
) on each characteristic:
I
Y Max
¼ nI
Max
þ nðn 2 1ÞI
Max
¼ n
2
I
Max
I
Max
¼ I
Y Max
=n
2
ð19Þ
2.4.2 Assumption 2. Random distribution of the
averages
In this hypothesis, the double product is equal to
zero.
Equation (17) becomes:
I
Y Max
¼
X
a
2
i
I
i Max
ð20Þ
Equation (20) is simplified in the case where
a
i
¼
1 and in the uniform distribution of inertia
(I
iMax
¼ I
Max
) on each characteristic.
I
Y
¼ nI
Max
I
Max
¼ I
Y
=n ð21Þ
2.4.3 Assumption 3. Unfavorable average shifts of k
sigma for all the characteristics
I
Y
¼
X
a
2
i
I
X
i
þ 2
X
a
i
a
j
d
i
d
j
I
Y
¼
X
a
2
i
I
iMax
þ 2
X
a
i
a
j
ð1 2 1=ð1 þ k
2
ÞÞ
ffiffiffiffiffiffiffiffiffiffi
I
i Max
p
ffiffiffiffiffiffiffiffiffiffi
I
jMax
p
ð22Þ
Equation (20) is simplified in the case where
a
i
¼
1 and in the uniform distribution of inertia
(I
iMax
¼ I
Max
) on each characteristic:
I
Y Max
¼ nI
X
þ nðn 2 1Þ 1 2
1
1 þ k
2

I
X
I
X
¼
I
Y Max
n
nk
2
þ1
1þk
2

ð23Þ
We will show that assumption 2 (random
distribution of averages) in the case of inertial
tolerancing is very robust even in hard unfavorable
conditions.
2.5 Comparison with traditional tolerancing
on an academic case (Figure 2)
In inertial tolerancing, we only retain the
assumption: random distribution of the averages.
This assumption is the best compromise between
the quality of the finished product and the
production cost. We use an academic case very
close to the Bisgaar’s ten washers example
(Bisgaard and Graves, 1997). We will retain a
uniform distribution of the tolerances on x
i
.
In traditional tolerancing, the clearance Y is
1 ^ 0:8: In the case of a centered population, a
Cpk ¼ 1:33 situation corresponds to the standard
deviation
s
¼ 0:2: In inertial tolerancing, the
condition will be I
Y
¼
s
2
Y
þ
d
2
Y

¼ 0:2
2
¼ 0:04
that one writes 1 (I 0.04). The targets are fixed in
the following way: X
1
¼ 9; X
225
¼ 2
2.5.1 Traditional tolerancing
In the case of the uniform distribution of the
tolerances we have (equations (2) and (5)):
.
worst case assumption X
i
¼ target ^ 0:08;
and
.
statistical assumption X
i
¼ Target ^ 0:35
2.5.2 Inertial tolerancing
In the case of the uniform distribution of the
tolerances based on the assumption of the random
distribution of the averages we have (equation
(21)): I
X
¼ I
Y
=5 ¼ 0:008; which corresponds to a
standard deviation
s
¼ 0:089 in the case of a
centered population.
2.5.3 Study of the extreme situations
In order to compare inertial and traditional
tolerancing, we will consider two extreme
situations:
(1) Centered situation (
d
X
i
¼ 0) with Cpk ¼ 1:33
for the traditional tolerancing and Cpi ¼ 1 for
the inertial tolerancing of all the
characteristics.
(2)
s
X
i
< 0 and the process is in limit of
acceptance (Cpk ¼ 1:33 and Cpi ¼ 1).
Figure 3 shows the limits of the traditional
tolerancing method. In the worst case, when all
elementary characteristics are centered, the
tolerances are too tight. In the statistical method,
when all elementary characteristics are decentered
in an unfavorable manner, the dependant variable
Y is outside of the tolerances.
As we see in Figure 3, when the Cpi index is
higher than 1 in both situations (
d
¼ 0 and
s
¼ 0)
Figure 2 Academic case of a mechanical assembly
Inertial tolerancing
Maurice Pillet
The TQM Magazine
Volume 16 · Number 3 · 2004 · 202-209
205
the dependant variable Y is acceptable. Inertial
tolerancing leads to minimizing production costs
(when the process is
d
¼ 0, the situation is similar
to classical statistical tolerancing) for a specified
level of quality (when the process
s
¼ 0;
d
Max
is
limited by the Cpi, and Y is more acceptable than
the classical worst case).
It is easy to generalize this academic case when
we have the following relationship:
Y ¼
X
n
i ¼1
x
i
ð24Þ
Case 1:
d
¼ 0
In this case, the accepted spread for the
elementary characteristics is very wide, it is the
same for classical statistical tolerancing.
Case 2:
s
¼ 0
In this case,
d
XMax
¼
ffiffiffiffiffiffiffiffiffiffiffiffi
I
XMax
p
on each
elementary characteristic x
i
. The resulting shift on
Y is equal to
d
Y Max
¼ n
d
XMax
:
3. Conformity and inertial tolerancing
3.1 Case of mixed batches
One of the disadvantages of the traditional
capability indicator Cpk appears when two batches
are mixed. By mixing two batches with an
acceptable capability (Cpk . 1:33), one can
obtain a non-acceptable capability for the mixed
batch (Cpk , 1:33).
This disadvantage is eliminated in the case of
inertial tolerance with the Cpi indicator. Indeed,
by mixing k batches of the same size n and from
capability Cpi
k
, one obtains a resulting batch such
as:
Cpi ¼ð1=kÞ
X
Cpi ð25Þ
Demonstration:
I ¼
1
kn
X
X
2
i
¼
1
kn
X
k
j¼1
ðX
i
2
X
j
þ
X
j
Þ
2
I ¼
1
kn
X
n
i ¼1
X
k
j¼1
ðX
i
2
X
j
Þ
2
þ
X
2
j
þ 2
X
j
ðX
i
2
X
j
Þ
hi
I ¼
1
k
X
s
2
k
þ
X
2
j

¼
1
k
X
I
j
ð26Þ
One changes immediately from equation (26) to
(25) by using equation (9). This property is
particularly interesting in the case of multi-
generator processes such as molding machines
with 64 cavities. Each cavity has a particular mean,
and it is impossible to adjust all cavities on the
target. If each cavity has an acceptable Cpi value,
then when all the production is mixed, total Cpi
will also be acceptable. It is not the case with
capability indicators such as Cpk or Cpm.
3.2 Inertial tolerancing and lot size
In the case of assembly, the decision about whether
a part conforms or not is not easy. Indeed,
although the part is assembled, the quality of the
assembled product will be the combination of
several characteristics. If one considers the case of
a characteristic near the specification limit, the
decision about conformity must two several known
or unknown elements into account:
Figure 3 Extreme situations
Inertial tolerancing
Maurice Pillet
The TQM Magazine
Volume 16 · Number 3 · 2004 · 202-209
206
(1) The distribution of the characteristics. The
decision should not be the same if the part
nearest to the specification limit is alone or if
100 percent of the production is also near the
specification limit.
(2) The distribution of the other important
characteristics of the assembly. In general, these
elements are unknown at the time the decision
is made.
Inertial tolerancing makes it possible to take these
various elements partly into account. Contrary to
the traditional methods, the goal is not to obtain a
level of quality measured by a percentage outside
tolerance, but to guarantee a low inertia around
the target (Figure 4).
... “Fuzzy tolerance” is a particularly interesting
point of inertial tolerance. In the case of unit
production, it guarantees the perfect conformity
of the production in the worst cases...
The inertial tolerancing leads to “fuzzy tolerances”
that vary according to the quantity of the parts
produced. To illustrate this point, let us imagine
the characteristic 9 (I 0.008) of our academic case
(Figure 2):
(1) Case of one part measured at 9.088. In this
case, the inertia for a part is equal to 0:088
2
¼
0:0077: The part is only just accepted.
(2) Now let us take the case of three parts: 9.00;
9.088; 9.125. Inertia is then I ¼ 0:0078; the
three parts are accepted. One part has an
individual inertia higher than 0.008.
(3) Finally, let us take the case of a batch of parts
averaging 9.05 and with a standard deviation
of 0.07. In this case I ¼ 0:0074; the batch is
also accepted even though it contains 28.6
percent of the products whose dimension is
higher than 9.0894 which is the approval limit
in the case of unit production.
This “fuzzy tolerance” is a particularly interesting
point of inertial tolerance. In the case of unit
production, it guarantees the perfect conformity of
the production in the worst cases. In the case of
series production, the inertial tolerance takes
account of the weak probability that at both
extremes of the tolerance limits will be assembled
together. Thus, with only one tolerance, one is able
to respond as well to cases of unit production as to
those in series production.
4. Inertial tolerancing in the case of
unilateral tolerance
4.1 Case where the ideal is zero
Traditional tolerancing in the higher unilateral
case such as the geometry or form defect consists
in fixing an upper limit specification that one
should not exceed. This method leads to illogical
results (Pillet, 1999, 2000) which privilege a batch
having a good Cpk, but with many parts near the
specification limits rather than a production
having a more modest Cpk, but with a greater
concentration of parts with a value close to zero
(ideal value).
In this case, the inertial tolerancing consists of
fixing the maximum inertia accepted compared to
zero. The batch will be accepted if its inertia is
lower than the inertia limit.
A machined element has a critical circularity
(I 0.01) (Figure 5). In the case of a measurement
of only one measured part with 0.12, the part is
refused because inertia is higher than 0.10. On the
other hand, if we consider a distribution
comprising the values with 0.14 but whose
distribution of the parts has a high density of
probability close to zero, one will be able to accept
the batch. The third batch will be refused,
although not including any value with 0.14.
However, as the distribution of the values will be
very offset compared to zero, it will lead to
unacceptable inertia.
4.2 Case where the ideal is a finished
value
One can quote, for example, an output that has
an ideal value of 100 percent or a temperature
having to be the coldest possible and whose ideal
should be absolute zero. In this case, one is
Figure 4 Conformity and inertial tolerancing
Figure 5 Case where the ideal is zero
Inertial tolerancing
Maurice Pillet
The TQM Magazine
Volume 16 · Number 3 · 2004 · 202-209
207
reduced to the preceding case by defining inertia as
the difference between the measured value and the
ideal value.
4.3 Case where the ideal is the infinite
One can quote, for example, a traction force which
one wishes to control. One is reduced to the case
where the ideal is zero, by defining a maximum
inertia on x
0
¼ 1=x; with x the measured
characteristic.
4.3.1 Application on a traction force after sticking
The sticking of shoes has a required inertia 0.03
(I 0.03) (Figure 6). As the example in Figure 6
shows, inertial tolerancing makes it possible to
interpret the will of the designer better by
considering the product function rather than just
the values themselves. In example #1, one part
measured to 4 is refused ðI ¼ð1=4Þ
2
¼ 0:0625 .
0:03Þ: For one par, minimum required is 5.78: (1/
5.78)
2
, 0.03. In examples #2 and #3, the
measured minimal value is 4, but it is easy to note
that the overall distribution #2 will give much
better satisfaction to the customers. Indeed in the
separation of a sole, it is necessary to consider the
combination between the force necessary to
wrench and the conditions of use imposed by the
owner. The probability of having the overlap of a
weak sticking and a severe use is much stronger in
case #3 than in case #2. A traditional tolerance
with a minimal tolerance of 3 daN/cm
2
would lead
to the conclusion of identical quality for both
batches (#2: Cpk ¼ 1:10; #3 Cpk ¼ 1:13).
5. Conclusion
In this paper, we have detailed the principle of
inertial tolerancing. This approach makes it
possible to view tolerancing differently. This
method has many advantages as follows:
.
In the case of an assembled product, the
inertial tolerancing leads to a better
compromise between the cost of production
and quality as opposed to the traditional
approaches.
.
The additivity property of inertia in the case of
mixed batches. The inertia of the mixed batch
will be the weighted average of elementary
inertias.
.
The ease of tolerancing bilateral, unilateral or
geometrical characteristics with the same
logic. In all cases, there is a unilateral
criterion: inertia.
.
The acceptance of a part takes account of the
batch size.
This new way of considering the tolerance marks
an evolution of the traditional way. It falls under a
logic that privileges centering on the target to the
detriment of counting not-in conformity
characteristics. The accent is on the finished
product, and not on the characteristic.
References
ANSI (1982), “Dimensioning and tolerancing”, ANSI Y14.5M-
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ASME (1994a), “Y14.5M-1994: Dimensioning and tolerancing:
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of process capability: CPM”,
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Technology
, Vol. 20 No. 3, pp. 162-75.
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the application of tolerance analysis to the design of
mechanical assemblies”,
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Vol. 3, pp. 23-37.
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Dearborn, MI.
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Statistical Quality Control
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New York, NY.
Graves, S. (1997), “How to reduce costs using a tolerance
analysis formula tailored to your organisation”, Report
No. 157, CQPI, Madison, WI.
Figure 6 Case where the ideal is the infinite
Inertial tolerancing
Maurice Pillet
The TQM Magazine
Volume 16 · Number 3 · 2004 · 202-209
208
Graves, S. (2001), “Tolerance analysis tailored to your
organization”,
Journal of Quality Technology
, Vol. 33 No. 3,
pp. 293-303.
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Quality
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, ISO, Geneva.
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(GPS), ISO,
Geneva.
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des produits et qualite
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des
caracte
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le
´
mentaires, l’objectif cible de la
conception a
`
la fabrication”, Congre
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Further reading
Bisgaard, S., Graves, S. and Shin, G. (2000), “Tolerancing
mechanical assemblies with CAD and DOE”,
Journal of
Quality Technology
, Vol. 32 No. 3, pp. 231-40.
Farnum, N. (1997), “Using Johnson curves to describe
non-normal process data”,
Quality Engineering
, Vol. 9
No. 2, pp. 329-36.
Pillet, M., Duret, D. and Sergent, A. (2001), “L’objectif cible
et la de
´
termination statistique des tole
´
rances”,
Actes
, Congre
`
s qualite
´
, Annecy, March, pp. 281-7.
Wheeler, D. (2000), “Normality and the process”,
Behavior
Chart
, Quality Press, Milwaukee, WI.
Inertial tolerancing
Maurice Pillet
The TQM Magazine
Volume 16 · Number 3 · 2004 · 202-209
209
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