Question 1.

A system has reliability function

R(t) = e^-(a+c)t+ e^-(b+c)t+ e^-(a+b+c)t

where

a = 0.05

b = 0.15

c = 0.13

Determine the mean time to failure.

Question 2.

A series system consists of two subsystems, A and B with independent failure times, arranged as shown below.

Both A and B follow a Weibull time to failure with the same shape parameter = 0.25.

A has characterstic life _A= 200 and B has charactestic life _B=100

Determine the mean time to failure of the system.

Question 3.

A parallel system consists of two subsystems, A and B with independent failure times.

If A has hazard rate 0.08 and B has hazard rate 0.03 .

Find the probability that the system survives until time t = 7.