Figure 1 shows a reliability diagram for a unit consisting of four elements which can be assumed to be operating in their useful life and to have constant failure rates.

The mean time to failure (MTTFs) for elements 1, 2, 3 and 4 are 25,000 hours, 15,000 hours, 15,000 hours and 5,000 hours, respectively.

i) Evaluate the reliability of each element after 1,000 hours operation.

ii) Evaluate the reliability of the unit consisting of the four combined elements after 1,000 hours operation.

iii) Evaluate the mean time between failures (MTBF) for the unit consisting of the four combined elements. (You are asked for the MTBF, because it is assumed that the unit can be repaired when any of its element fails.)

b) Figure 2 shows a reliability diagram for a system element consisting of components having reliabilities R1 = 0.95, R2 = 0.85, R3 = 0.98 and R4 = 0.99. Calculate the overall reliability of the system.