Tolerances are a very important property of a design. This paper presents a method for simulating tolerances in signal processing and control systems on the system level using affine arithmetic. The method is compard to simulation based on interval arithmetic or Monte-Carlo method and goes into details of the shortcomings of interval arithmetic. An introduction to affine arithmetic is given and...

The currently adopted notion of a tolerance in combinatorial optimization is defined referring to an arbitrarily chosen optimal solution, i.e., locally. In this paper we introduce global tolerances with respect to the set of all optimal solutions, and show that the assumption of nonembededdness of the set of feasible solutions in the provided relations between the extremal values of upper and l...

During the design of new technical systems, their manufacturing tolerances (i.e. system parameter uncertainties) should be determined basically by working requirements of the system and technological possibilities of the manufacturers. Therefore the determination of manufacturing tolerances can be a very important and difficult task. It is possible that system output parameter values are inadeq...

The geographic ranges of closely related species can vary dramatically, yet we do not fully grasp the mechanisms underlying such variation. The niche breadth hypothesis posits that species that have evolved broad environmental tolerances can achieve larger geographic ranges than species with narrow environmental tolerances. In turn, plasticity and genetic variation in ecologically important tra...

Whenever we base some decision on a comparison of numerical values, we must consider the impurity of those values. Thus, if a decision depends on whether v = 0, we instead test if |v| ≤ τ , where τ is some small value called a tolerance. More generally, for a particular comparison of the form v = V , we define two tolerances: absolute and relative, denoted τa and τr, respectively. Then, we test...

In bunch compressors for SASE-FEL facilities, the projected transverse emittance can be diluted by magnetic multipole component errors in dipoles and dipole misalignments as well as by coherent synchrotron radiation (CSR). In this paper, we describe the multipole field tolerances and the misalignment tolerances of the first bunch compressor (BC2) for the TESLA Test Facility Phase-2 (TTF-2).