File:Standardabweichung black.png
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- Author: Patrick-Emil Zörner User:Paddy
- uploaded as de:Bild:Standardabweichung black.png by Paddy on de-WP 2004-07-03, 16:18 with comment: Standartabweichung Black
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[edit](only changed licence tags, removed double licence tag)
- Beschreibung: de:Standardabweichung
- Quelle: Selber erstellt mit einem Tabellenkalkulationsprogramm
- Zeichner: Patrick-Emil Zörner (User:Paddy)
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Trägt man auf einfach logarithmischen Wahrscheinlichkeitspapier F(T) in % über der Lebensdauer in Stunden auf, so erhält man eine Gerade. An dem Funktionswert F(t)=50 % kann man die mittlere Lebensdauer ablesen. Die Standardabweichung der Lognormalverteilung entspricht der Steigung der Geraden. Löst man den Term mit u aus der 2. Gleichung bei Image:Lognormal_Black.png nach σ auf und setzt u=-1 erhält man
In der Zeitspanne t16 sind analog zu t50 16 % aller Strukturen ausgefallen. Dieselbe Gerade erhält man, wenn man mit den ermittelten Ausfallzeiten in der selben Grafik die Ausgleichsgerade konstruiert.
Die Fehlerrate λ ist gegeben durch:
Während p(t) den Anteil angibt, der im Zeitintervall (t,t+dt) ausfällt, gibt λ(t) die Wahrscheinlichkeit für den Ausfall einer Teststruktur in diesem Zeitintervall, bezogen auf die Zahl der noch intakten Strukturen, an. Dieser Unterschied macht \lambda unempfindlich gegen Frühausfälle. Hat beispielsweise eine Anzahl von N Strukturen einen Schaden, welcher einen Frühausfall bewirkt, so wird nach den Anfangsausfällen p(t) um den Faktor (1-N) reduziert. Dies passiert nicht, weil sich die langzeit Verläßlichkeit verbessert hat, sondern weil weniger Strukturen übrig sind, um auszufallen.
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[edit]Author: Patrick-Emil Zörner (User:Paddy}; uploaded by Paddy on de-WP 2004-07-03, 16:18 with comment: Standartabweichung Black
original version history
[edit]- 02:02, 11. Feb 2006 Paddy
- 16:46, 27. Jan 2005 APPER
- (m) 15:57, 4. Jul 2004 Anathema
- (m) 15:52, 4. Jul 2004 Danimo
- 15:28, 4. Jul 2004 Paddy (Beschreibung)
- 16:18, 3. Jul 2004 Paddy (Standartabweichung Black)
Changes
[edit]- image: changed with upload on commons: removed wrong square brackets around the unit symbols
- description: only changed licence tags, removed double licence tag)
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 09:39, 11 March 2006 | ![]() | 708 × 588 (3 KB) | Georg Slickers (talk | contribs) | Author: Patrick-Emil Zörner User:Paddy, {{GFDL}} {{FWL}} {{cc-by-sa-2.0-de}}; uploaded by Paddy on de-WP 2004-07-03, 16:18 with comment: ''Standartabweichung Black'' |
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File change date and time | 09:19, 11 March 2006 |