11 weibull destribution 2 (2)

11 weibull destribution 2 (2) - Preliminary presentation...

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MFG5350 1 October 13, 2008 (Monday) Preliminary presentation for project
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MFG5350 2 October 20, 2008 (Monday) Mid-term exam
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MFG5350 3 Due Oct 10 (next Friday) before 5:00PM Homework 3
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MFG5350 4 The Weibull Distribution (continued)
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MFG5350 5 Time Dependent Failure Mode & Reliability 0 t ; 0 > 0, > ; t = (t) 1 - where is the shape parameter and is the characteristic life t dt t - e e = R(t) 1 t 0 '
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MFG5350 6 e t = dt dR(t) - = f(t) t - 1 - The Probability Density Function (PDF) -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 t f(t) 0.5 1.5 2.0 4.0 Beta Theta = 2 : the shape parameter.
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MFG5350 7 The Hazard Rate Function 0 1 2 3 4 5 6 0.0 1.0 2.0 3.0 4.0 5.0 6.0 t Hazard Rate 0.5 1.5 2.0 4.0 Beta Theta = 2 f(t) / R(t) 0 t ; 0 > 0, > ; t = (t) 1 -
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MFG5350 8 The Bathtub Curve
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MFG5350 9 Student Exercise - Weibull A certain brand lightning arrester has a Weibull failure distribution with a shape parameter of 2.4 and a characteristic life of 10 years. Find: a. R(5 yrs) b. MTTF c. Standard deviation d. Median and Mode e. 99% and 95% design life f. R(5|5)
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MFG5350 10 Student Exercise - solution 8274 . ) 5 ( . 4 . 2 10 / 5 e R a b MTTF yrs . ( / . ) ( . ) (. ) . 10 1 1 2 4 10 142 10 88636 886 2 2 2 )] 42 . 1 ( [ ) 4 . 2 / 2 1 ( . c or =3.93 yrs =
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MFG5350 11 Student Exercise - solution (continued) . 0 . 8 4 . 2 / 1 1 10 4 . 2 / 1 mod yr t e 4 . 2 / 1 69315 . 0 . med t d yr t e 5 . 1 99 . 0 ln . 4 . 2 / 1 . yr t 9 . 2 95 . 0 4 . 2 / 1 .
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MFG5350 12 Student Exercise - solution (continued) 2.4 10 10 (10) . (5| 5) (5) .8274 .3679 .4446 .8274 Re fR R
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MFG5350 13 In Summary R t e t ( ) t e t R ) ( t t R 1 ) ( med t t s t R ln 1 1 ) ( Exponential Weibull Normal Lognormal MTTF 1/ 1 1 t e s 2 2 / Reliability
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MFG5350 14 Failure Modes n i n i i i i t t t 1 1 1 1 1 ) ( which is a Weibull hazard rate function with a shape parameter of and a characteristic life of / 1 1 1 n i i
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MFG5350 15
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This note was uploaded on 04/25/2010 for the course IE 654 taught by Professor Smith during the Spring '10 term at 카이스트, 한국과학기술원.

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11 weibull destribution 2 (2) - Preliminary presentation...

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