A Note on the Convolution of the Uniform and Related Distributions and Their Use in Quality Control

Killmann Frank and Elart von Collani
Additional contact information
Killmann Frank: Deutsche Bank AG, Taunusanlage 12, D-60262 Frankfurt, Germany
Elart von Collani: Universität Würzburg, Sanderring 2, D-97070 Würzburg, Germany. collani@mathematik.uni-wuerzburg.de

Stochastics and Quality Control, 2001, vol. 16, issue 1, 17-41

Abstract: Consider a product with quality characteristic X. Assume that the product is composed of n parts each with quality characteristic Xi, and and letX = X1 + . . . +XnAssume that there is a lower specification L and an upper specification U for X. Then the problem arises how to select suitable specifications for the quality characteristics Xi of the parts. If the type of distributions of the partial quality characteristics Xi are known, then for solving the specification problem, the distribution of X = X1 + . . . + Xn is needed.In case of measurable quality features, usually the normal model is assumed for the Xi and the problem of deriving the distribution of X is solved in the well-known way. However, generally the only feature of Xi which is known with certainty is its bounded support, which follows from technical conditions. In such a case the normal approximation which is based on an unbounded support of each Xi may lead to a distribution of X which does not reflect reality sufficiently well.In this paper, the uniform or a related distribution is assumed for the partial quality characteristics and an explicit expression for the distribution of the sum X is derived. The usefulness of the result is illustrated by an example taken from industrial practice.

Keywords: Uniform Distribution; Convolution; Statistical Tolerancing; Production-oriented Tolerancing (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (3)

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DOI: 10.1515/EQC.2001.17

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