page 1 Statistical tolerancing, Inertial tolerancing, Acceptance sampling, (Mechanical assembly) Maurice PILLET* Pierre Antoine ADRAGNA** Frédéric GERMAIN** INERTIAL TOLERANCING : THE SORTING PROBLEM Abstract Inertial tolerancing presents a new way to define the conformity of a characteristic without defining the specification interval as it is traditionally the case. Conformity is defined by "inertia" (Taguchi loss function [5]) around the target. The principle of inertial tolerancing consists of tolerancing the mean square deviation from the target. The tolerances are not represented by the traditional [Min Max] interval. We have shown [1] [3] that this tolerancing method offers numerous advantages in term of Quality/Cost ratio, but it raises severe problems when batches are not acceptable. In these cases with traditional tolerancing, the products are sorted in order to eliminate each part outside tolerance. In inertial tolerancing, the problem consist in eliminating products the most far from the target to obtain an inertia corresponding to the specifications. The sorting limits depend on three elements: standard deviation, deviation from the target and distribution law. In this paper, the proposed method differentiates two situations. In the first one the distribution law is considered as a uniform law [a b] not centred on the target. In the second one we consider a normal law with a standard deviation  en a deviation from the target  Analytical solution is given for the first situation. In the second situation, analytical solution is impossible and we propose a very quick algorithm allowing resolving this problem. An Excel solution is presented. The proposed solution can be used in the case of traditional tolerancing when the conformity is decided on the capability index Cpm [2] 1. INTRODUCTION Inertial tolerancing [1] [3], proposes an alternative to the traditional tolerancing method which expresses conformity as an acceptance zone. Inertial tolerance is based on the Taguchi loss function [4] [5] which express the financial loss related to a difference between the required target and value measured by the relation:   2 Target X i X k L   (1) * Laboratoire LISTIC - Université de Savoie – ESIA – IUT Annecy - B.P. 806 - 74016 Annecy Cedex maurice.pillet@univ-savoie.fr ** Laboratoire LISTIC - Université de Savoie – ESIA – IUT Annecy - B.P. 806 - 74016 Annecy Cedex pierre-antoine.adragna@univ-savoie.fr; frederic.germain@univ-savoie.fr Machine Engineering : Manufacturing Accuracy Increasing Problems, optimization, Vol. 6, No. 1, 2006, pp. 95‐102.