Vergleich von Approximationen für die auf der hypergeometrischen Verteilung beruhenden Operationscharakteristik
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Diplomarbeit aus dem Jahr 2011 im Fachbereich Mathematik - Statistik, Note: 1.0, Universität Hamburg (Institut für Statistik und Ökonometrie), Sprache: Deutsch, Abstract: Der wissenschaftliche Zweig der statistischen Qualitätskontrolle im Rahmen der Betriebswirtschaftslehre beschäftigt sich unter Anderem mit der Abbildung von Situationen der Eingangs- und Endkontrolle einer Warenpartie in einem Unternehmen und dient dabei der Entscheidungsunterstützung, ob eine solche Warenpartie anzunehmen oder abzulehnen ist. Die Warenkontrolle verläuft in einem Unternehmen normalerweise anhand eines Stichprobenverfahrens, indem aus Kosten- und Zeitgründen nicht die gesamte Warenpartie, sondern nur ein Teil dieser Partie auf ihren Ausschussanteil hin untersucht wird. Je nachdem, wie hoch dieser Ausschussanteil ausfällt, kann dann über eine Annahme oder eine Ablehnung der gesamten Warenpartie entschieden werden. Dieser Vorgang lässt sich gut unter Verwendung des statistischen Modells einer Zufallsstichprobe ohne Zurücklegen abbilden. Die Entscheidung über die Annahme einer Warenpartie hängt dann von der Höhe einer statistischen Grö e ab, der sog. Operationscharakteristik, die als gebräuchlicher Begriff für die Annahmewahrscheinlichkeit einer Warenpartie verwendet wird. Da das Modell einer Stichprobe ohne Zurücklegen bei der Herleitung der hypergeometrischen Verteilung zugrunde gelegt wird, spielt diese insofern für die statistische Qualitätskontrolle eine zentrale Rolle, als dass auf ihrer Basis auch die hypergeometrische Operationscharakteristik gebildet wird, deren Formel die exakte Annahmewahrscheinlichkeit einer Warenpartie liefert. Aufgrund ihrer Komplexität lässt sich die hypergeometrische Operationscharakteristik allerdings nicht immer exakt berechnen. Eine Abhilfe dieser Problematik können zwei geeignete Näherungen der hypergeometrischen Operationscharakteristik bilden: Die binomiale und die Poisson'sche Operationscharakteristik, die, wie ihr Name bereits erahnen lässt, a
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