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Zuverlässigkeitstheorie: Eine Einführung Über Mittelwerte Von Binären Zufallsprozessen by Winfrid G. Schneeweiss

Zuverlässigkeitstheorie: Eine Einführung Über Mittelwerte Von Binären Zufallsprozessen

by Winfrid G. Schneeweiss
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Book cover type: Paperback
  • ISBN13: 9783540061939
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 144
  • Original Price: EUR 51.39
  • Language: German
  • Edition: N/A
  • Item Weight: 259 grams
  • BISAC Subject(s): General

Infolge der beschleunigt vorangetriebenen Automatisierung in unserer Zivilisa- tion erleben wir eine Bliltezeit der Zuverliissigkeitstheorie. Dabei ist es ver- wunderlich, daB selbst in der mehr theoretisch orientierten Literatur der groBe praktische Nutzen von Indikatorfunktionen, die die Wahrscheinlichkeitstheorie schon lange kennt, nicht oder nur teilweise ausgeschopft wird. Das soll im fol- genden nachgeholt werden. Die Zuverliissigkeitstheorie beschiiftigt sich mit der Berechnung von Wahrschein- lichkeiten von zunehmend komplexen Ereignissen sowie von Verteilungen, nach denen diese Ereignisse andauern, mittels der entsprechenden Daten von einfa- cheren Ereignissen. Dabei kommt es leicht zu unilbersichtlichen Rechnungen, wenn die einfachen Ereignisse sich nicht gegenseitig ausschlieBen, so daB die Wahrscheinlichkeit einer "Ereignissumme" nicht gleich der Summe der Wahr- scheinlichkeiten der Einzelereignisse ist. Wenn man dagegen den betrachteten Ereignissen Anzeige-Zahlen so zuordnet, daB diese Zahlen 1 sind, wenn das betreffende Ereignis eingetreten ist, und 0 sonst, dann hat man zuniichst eine interessante neue Moglichkeit fUr die Zustandsbeschreibung eines Systems ge- funden. Dies bringt Stormer [1] sehr ausfilhrlich; be30nders in Kap. 5. Wich- tig ist nun die Tatsache, daB die Wahrscheinlichkeit filr den Wert 1 solcher boole- schen Variablen einfach durch Bildung des Erwartungswerts gefunden werden kann, denn der mathematische Erwartungswert einer Zufallsvariablen ist gleich der Summe der mit den Auftrittswahrscheinlichkeiten gewogenen Werte der Va- riablen. (Dies wird zwar bei Bar low / Pro s c han erwiihnt, aber nicht kon- sequent weiterverfolgt.

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