# 4 (2) - Homework#1 Due(Friday 5:00PM To drop off at A117 or...

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MFG5350 1 Due September 12, 2008 (Friday) 5:00PM Homework #1 To drop off at A117, or email to jzhang 2 @utep.edu

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MFG5350 2 Failure Rate or Hazard Rate Function t) + R(t - R(t) = t} + t T {t Prob R(t) t) + R(t - R(t) = t} T t + t T {t Prob | t R(t) t) + R(t - R(t) R(t) 1 t R(t)] - t) + [R(t - = (t) 0 t Lim R(t) f(t) = R(t) 1 dt dR(t) - = (t) is called the instantaneous hazard rate or failure rate function. When it is increasing (decreasing or constant), it is called IFR (DFR or CFR).
MFG5350 3 Example #5 - hazard rate function ( ) / / / t t t t t t t 50 1 100 50 100 100 2 100 2 2 2 10 yr t (t) IFR R t t t yrs ( ) ; 1 100 0 10 2

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MFG5350 4 t dt t e t R 0 ' ) ' ( ) ( Example: 2 0 01 . ' ' 02 . ) ( , 02 . ) ( t dt t e e t R then t t t
MFG5350 5 The Bathtub Curve

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MFG5350 6 More on the Bathtub Curve Burn-in Useful Life Wearout Characterized by DFR CFR IFR Caused by Manufacturing defects Environment Fatigue Welding flaws, Cracks, Random loads Corrosion Defective parts, Poor Human error
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4 (2) - Homework#1 Due(Friday 5:00PM To drop off at A117 or...

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