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In graph theory, a tolerance graph is an undirected graph in which every vertex can be represented by a closed interval and a real number called its tolerance, in such a way that two vertices are adjacent in the graph whenever their intervals overlap in a length that is at least the minimum of their two tolerances. [1]
A tolerance interval (TI) is a statistical interval within which, with some confidence level, a specified sampled proportion of a population falls. "More specifically, a 100× p %/100×(1−α) tolerance interval provides limits within which at least a certain proportion ( p ) of the population falls with a given level of confidence (1−α)."
Prefix letters I, L, O, Q and W are not used to avoid confusion. Of these, the letter prefixes H and h are easiest to explain as the tolerance lies entirely on one side of the nominal size. A hole dimensioned at 4 H7 may range from 4.00 - 4.012 mm, and a shaft at 4 h7 may range from 3.988 - 4.00 mm.
The normal distribution is NOT assumed nor required in the calculation of control limits. Thus making the IndX/mR chart a very robust tool. This is demonstrated by Wheeler using real-world data [4], [5] and for a number of highly non-normal probability distributions.
Example of true position geometric control defined by basic dimensions and datum features. Geometric dimensioning and tolerancing (GD&T) is a system for defining and communicating engineering tolerances via a symbolic language on engineering drawings and computer-generated 3D models that describes a physical object's nominal geometry and the permissible variation thereof.
The range of W 0 is inside the C-shaped black curve. The range of each of the other branches is a band between two black curves that represent points on the negative real axis (a black curve representing the positive real axis runs through the middle of each such band). Source Created in mathematica 9.0 Date 2017-10-06 Author Sławomir Biały ...
For example, if a shaft with a nominal diameter of 10 mm is to have a sliding fit within a hole, the shaft might be specified with a tolerance range from 9.964 to 10 mm (i.e., a zero fundamental deviation, but a lower deviation of 0.036 mm) and the hole might be specified with a tolerance range from 10.04 mm to 10.076 mm (0.04 mm fundamental ...
Tolerance analysis is the general term for activities related to the study of accumulated variation in mechanical parts and assemblies. Its methods may be used on other types of systems subject to accumulated variation, such as mechanical and electrical systems.