Question

Consider a CFR device having a failure rate (2) of 0.0002 failure per hr. What is the MTTF of the device? ans: 5000 hr Suppose the device has survived for 6000 hr. What is the expected value of the remaining life of the device? What is the probability that the device survives an additional 10000 hr? ans: 5000 hr; 0.135

Answer 1

a) We are given the failure rate here as 0.0002 / hr. Therefore the mean time to failure here is computed as:

= 1 / Rate of failure

= 1 / 0.0002

= 5000 hrs.

Therefore 50000 hrs is the mean time to failure here.

b) Given that the device has survived for 6000 hours, the expected time to failure still remains the same as initial, because the exponential distribution follows a memoryless property. Therefore 5000 hours is the expected time to failure.

c) The probability that the device survives an additional 10000 hours is computed here as:

$P(T > 10000) = \int_{10000}^{\infty } 0.0002e^{-0.002t}dt = e^{-0.0002*10000} = 0.1353$

Therefore 0.1353 is the required probability here.