Interest of inertial tolerancing for variability control in assembled systems
PILLET Maurice (1) AVRILLON Laetitia (1,2)
(1) LISTIC/University of Savoy
BP 806
74016 Annecy Cedex France
Telephone: (+33) 4 50 09 65 80 Fax: (+33) 4 50 09 65 90
laetitia. avrillon@univ-savoie.fr
maurice. pillet@univ-savoie.fr
(2) TRIXELL
Z. I Centr' Alp 460, rue de Pommarin
38430 Moirans France
Abstract:
Quality on the finished-product is the combinatory of quality on each part of the product. That is to say the slightest
variability on an elementary part causes variability on the end. However, parts are manufactured independently and
they are themselves the resultant of a combinatory of elementary characteristics. Moreover, it is impossible to know and
to monitor all these characteristics for nature or money reasons. So, how guarantee conformity on the finishedproduct?
If we manage to guarantee independently variability control on all characteristics known, we make our product robust
regard to the uncontrollable characteristics as environmental conditions. Our proposition is to fix a maximal inertia
around the target for each elementary characteristic instead of two extreme limits. This new way of tolerancing, called
inertial tolerancing, allows us to guarantee in an independent manner the centering of all the characteristics
monitored, thus the product becomes robust. Inertial tolerancing induces many cultural changes: a new view of
conformity, a new view of capability (Cpi) and the focus on centering.
Keywords: Capability, Conformity, Inertial Tolerancing, Statistical Tolerancing, Taguchi Loss Function, Worst case
Tolerancing.
1. Introduction: Assembled systems and
variability
In the case of assembled systems or more generally in
the case of products resulting of a lot of characteristics
Xi, a few measurements Yj on the final product can be
determined as Critical to Quality. We suppose that the
final functional condition Y of all elementary
characteristics Xi must be decomposed into a first order
approximation:
?=
+ =
n
i
i i X Y
1
0 a a [E1]
A measurement Y depends on a lot of
characteristics. Let us take the example of the motor
yield variability for a motor given; its consumption
depends on a vast number of Xi as dimensional,
geometric and electric characteristics but also
environmental and working conditions. Control of its
yield goes through control of these Xi.
To establish the relation between Y and Xi, we must
know the coefficients ai but above all we must identify
all the Xi. Now, it is quietly impossible to have the
exhaustive list of the elementary characteristics.
Indeed, even in the case of old products, new Xi
arealways be discovered, after a new important
problem in production for example. Furthermore, even
if the complete list of the characteristics could be
obtained, it would be impossible to control all the Xi for
many reasons. First, some Xi are uncontrollable
because of their nature: the weather for example.
Secondly, certain Xi monitoring is too expansive to be
implemented.
Variability control on a measurement Y requires to
control variability on each elementary characteristic Xi
regardless of each others. Operator A who makes
characteristic Xk doesn’t know of course what makes
operator B. To reach this objective of independence,
we establish two principles that are not always well
applied in industries:
Principle 1: centering on the target. It is desirable to
center all the characteristics on their target. This action
has priority on the improvement of "short term"
dispersions.
Demonstration
Case 1: action on the centering of a characteristic
We suppose that E(Xk) is not centered on the target
C(Xk) (whatever the k).
E(Xk) = C(Xk) + d
E(Xi) = C(Xi) for i ? k
d a
a a
k
i i
Y C Y E
X E Y E
+ =
+ = ?
) ( ) (
) ( ) ( 0 [E2]
.....