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Failure rate of a system at time 't' 
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#1
Mar2111, 07:36 PM

P: 32

I need to solve the following problem for a school assignment.
Let λ(t) denote the failuer rate of a system at time 't'. The failure rate is simple the number of failures in unit time. For example, if the unit time is one day, then λ is the average of failures per day. Let μ(t) denote the total number of failures from the first release (time t=0) until the current time, 't'. Then we have (1) λ= dμ/dt (2) μ = ∫λ(T) where the limits of integration are T=0 (lower) and T=t (upper) Two models are used for estimating λ and μ. In the forumlae below, λ0 is the failure rate at time t=0, and α and β are constants λ=λ0(1μ/α) λ=λ0e^ β μ Use (1) or (2) to find λ and μ as functions of time for each model. .....I just need some direction. Thanks! 


#2
Mar2111, 07:56 PM

PF Gold
P: 1,941

[tex]\lambda = \lambda_0 \left(1\frac{\mu}{\alpha}\right)[/tex] You should be able to substitute λ=dμ/dt and get a seperable differential equation in μ. Then you differentiate that equation to get λ. So you just need to solve: [tex]\frac{d\mu}{dt} = \lambda_0 \left(1\frac{\mu}{\alpha}\right)[/tex] 


#3
Mar2111, 08:06 PM

P: 32

so i just differentiate with respect to μ?



#4
Mar2111, 09:46 PM

P: 32

Failure rate of a system at time 't'
so the resulting integration would be:
α ln (μ α) evaluated at 0 and 't' correct? 


#5
Mar2111, 10:05 PM

PF Gold
P: 1,941

Well, don't EVALUATE it at those two points. Instead, set that equal to t+C.



#6
Mar2111, 10:22 PM

P: 610

francis has started two threads for the same question. another thread at
http://www.physicsforums.com/showthread.php?t=483125 I am answering the same question at this thread. Beware francis 


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