Question: 7. (a) Define the terms (i) reliability; (ii) active redundancy; and (iii) standby redundancy. (4 marks) (6) Determine the reliability after 1 year of a

7. (a) Define the terms (i) reliability; (ii)

7. (a) Define the terms (i) reliability; (ii) active redundancy; and (iii) standby redundancy. (4 marks) (6) Determine the reliability after 1 year of a system consisting of 3 identical pumps connected in parallel and 2 identical boilers also connected in parallel. For the system to operate normally, only 2 of the pumps and both boilers are required to work. All pumps and boilers fail randomly, and the pumps are operating in active redundancy mode. The MTBF for pumps and boilers are 8000 hours and 9500 hours, respectively. (8 marks) (c) The general equation for active redundancy of parallel networks with m energized identical components of which n must work for system to operate at design conditions is: n R(t) = {x! (n 1)? ! k (e-le)" (1 -2)(n-K) k=m When a hospital that has five identical medical air compressor and requires three compressors to achieve peak demand, derive a reliability equation for this situation. (4 marks) (d) It is known that a manufacturing process produces 10% of sub-standard pipe fittings. If a sample of 30 fittings is taken at random from a box containing 1000 fittings, find the probability of the sample containing two or more sub-standard fittings. (4 marks) m

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