Question

Compute each of the following quantities assuming that the time to failure of the system is exponential with a mean time to failure of 1000 h and a guaranteed life of 200 h. Be sure to include units where appropriate.

(a) the system's failure rate
(b) the system's 100-h reliability
(c) the system's 300-h reliability
(d) the system's 700-h reliability given survival up to 600 h
(e) the system's design life for a 95% reliability.

Answer 1

The system's failure rate is 0.001 failures per hour. The reliability at various hours is calculated using the exponential distribution reliability function, and the design life for a 95% reliability is determined by solving the inverse of this function.

Step-by-step explanation:

The the system's failure rate for an exponential distribution with a mean time to failure of 1000 hours is the inverse of the mean time to failure, which is 0.001 failures per hour. The reliability function for an exponential distribution is given by R(t) = e-λt, where λ is the failure rate and t is the time.

For 100-h reliability, we calculate R(100) = e-0.001*100 = e-0.1. For 300-h reliability, R(300) = e-0.001*300 = e-0.3. To find the 700-h reliability given survival up to 600 h, we compute R(700|600) = R(700) / R(600) = e-0.001*(700-600) = e-0.1. The design life for a 95% reliability is found by solving R(t) = 0.95 for t, which gives t = -ln(0.95)/0.001.