Suppose a component is over stressed such that it reaches its faliure point afte
ID: 2941668 • Letter: S
Question
Suppose a component is over stressed such that it reaches its faliure point after 3000 hrs operation when dissipating 200 watts. Under normal operating conditions, the component dissicipates much less than 1 watt and lasts mant tens of thousands of hours without failing.Suppose also that the relationship between dissipated power and the faliure rate is an exponential one.
1) After how many hours would the component reach its faliure point when dissipating 120 watts?
2) After how many hours when dissipating 100 watts?
Please use as much detail as u can. :)
(Is it possible to do this problem using y=Ae^(kt) and f(t)=e^(-t/R)?)
Explanation / Answer
Suppose a component is over stressed such that it reaches its faliure point after 3000 hrs operation when dissipating 200 watts. Under normal operating conditions, the component dissicipates much less than 1 watt and lasts mant tens of thousands of hours without failing.
Suppose also that the relationship between dissipated power and the faliure rate is an exponential one.
1) After how many hours would the component reach its faliure point when dissipating 120 watts?
2) After how many hours when dissipating 100 watts?
Please use as much detail as u can. :)
(Is it possible to do this problem using y=Ae^(kt) and f(t)=e^(-t/R)?)
Relationship between dissipated power and the faliure rate is an exponential one....so...
T=FAILURE TIME IN HRS.........P=DISSIPATED POWER
IN WATTS
P=A*E^(K/T)................1
WHERE A AND K ARE CONSTANTS.........
faliure point after T=3000 hrs operation when dissipating P=200 watts.
SINCE THERE IS ONLY ONE DATA POINT WE HAVE TO ASSUME EITHER A OR K .....ASSUMING A=1
200=E^(K/T)...............2
K=LN[200]*3000 =15894.9521
P=[E^(15894.9521/T)].............................3
1) After how many hours would the component reach its faliure point when dissipating 120 watts?
T=?..........P=120 W.....
120=[E^(15894.9521/T)]
T=3320.1 HRS .
2) After how many hours when dissipating 100 watts?
100=E^(15894.9521/T)
T=3451.545 HRS
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