In this paper, we consider tolerances induced by irredundant coverings. Each tolerance R on U determines a quasiorder .R by setting x .R y if and only if R(x) ⊆ R(y). We prove that for a tolerance R induced by a covering H of U , the covering H is irredundant if and only if the quasiordered set (U,.R) is bounded by minimal elements and the tolerance R coincides with the product &R ◦.R. We also ...

We show that for any tolerance R on U , the ordered sets of lower and upper rough approximations determined by R form ortholattices. These ortholattices are completely distributive, thus forming atomistic Boolean lattices, if and only if R is induced by an irredundant covering of U , and in such a case, the atoms of these Boolean lattices are described. We prove that the ordered set RS of rough...

Analysis and allocation of tolerance are the typical problems in tolerance planning for the assembly and its components. This paper presents the developed simulator which is able to assist in solving tolerance planning problems in production processes, both in manufacturing and assembly processes. The paper also shows the benefits of this simulator which leads to quality characterisation and im...

Greenwich and Jahr-Schaffrath (1995) introduced an index Cpp, a simple transformation of the index C∗ pm, which provides an uncontaminated separation between information concerning the process accuracy and process precision. Unfortunately, the index Cpp inconsistently measures process capability in many cases and thus reflects process potential and performance inaccurately. In this paper, we co...

According to the American Society of Mechanical Engineers [1], tolerance is the total amount by which a specific dimension is permitted to vary from its nominal value. Tolerance allocation, also called tolerance synthesis, is carried out at the process planning stage in order to distribute the component’s design-specified tolerances, also called blue print (BP) tolerances, among the various ope...

Abstract This work focuses on the impact of build orientation additively manufactured waveguide-based hybrid couplers for D-band frequency range and relates it to other sources uncertainty within overall manufacturing process measurement instrumentation range. The designed specimens are first printed from UV curable photopolymer resin subsequently metal coated by an electroless silver plating p...

The rapid proliferation of coordinate measuring machines (CMMs) triggered the need for precise and rigorous formulations of each tolerance concept. In this paper, we employ the concept of con guration space of symmetric features to de ne each type of datum features and orientation tolerances. The establishment of datum features and orientation tolerances are formulated in an linear programming ...

We study error propagation through implicit geometric problems by linearizing and estimating the linearization error. The method is particularly useful for quadratic constraints, which turns out to be no big restriction for many geometric problems in applications.