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Question 4.2: Suppose the population of devices is described by the life d...

Suppose the population of devices is described by the life distribution F(t)=1-exp(-0.0001t).
1. What is the probability that a new device will fail after 1000 h? After 5000 h? Between these times?
2. What is the failure rate at 1000 h? After 5000 h?

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  1. By substitution, F(t)=1-exp[-0.0001(1000)]=0.095. Similarly, at 5000h, F(t)=0.39. The probability of device failure between 1000 and 5000 h is F(5000)-F(1000)=0.39-0.095=0.30.
  2. f(t)=dF(t)/dt=0.0001 \ exp(-0.0001). The failure rate is \lambda(t)=f(t)/[1-F(t)]=0.0001 \ exp(-0.0001t)/exp(-0.000t)=0.0001. For this distribution the failure rate is seen to be time-independent.

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