The asymmetric quadratic loss function 5 punishes the

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Unformatted text preview: is computationally a much harder problem than in the general case. 2. REVIEW OF TOLERANCE ANALYSIS AND ALLOCATION METHODS This section reviews earlier and related work on the subject. Many authors have studied tolerance allocation (also called tolerance synthesis) over a long time period. We first supply a short introduction to tolerance analysis. 2.1. Tolerance analysis Let a product be defined by n dimensions represented by stochastic variables x1,…,xn, where each xi is related to a statistical distribution with expected value µi and standard deviation σi. Let Di be the nominal value for xi and ti its tolerance, such that xi ∈ (Di-ti, Di+ti) must hold. Furthermore, let y be a critical measure on the product. The relation between y and x1,…,xn can be described by an assembly function f: y = f ( x1 ,..., xn ). f is often approximated by a linearization about the expectance values (µ1,…,µn): (1) y = f ( µ1 ,..., µ n ) + ∑ ai ( xi − µi ) , i =1 n (2) ∂f ( µi ) are called the sensitivity coefficients. The assembled tolerance τ for ∂xi y can now be estimated (statistically) by...
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