Total = 3 marks The figure shows a reliability block diagram with 3 components. Component B and C are in parallel. Component A is in series with the B.C combination. A B Assume the mission time is 120 hours. Assume the time to failure of the components are independent. a) Design 1: Assume the probability distribution of the time to failure of the A, B and C components are identical and are described by a constant hazard rate with a mean life of 768hrs. [a] (1 mark) Calculate the system reliability of Design 1 to 3dp. b) Design 2: Assume the probability distribution of the time to failure of components is as follows. : [b] (1 mark) The probability distributions of components B and C are each described by a constant hazard rate with a mean life of 768 h. In other words R_B(150) = R_C(150) The probability distribution of component A is described by a Weibull distribution with shape parameter 2.2and characteristic life of 400 hours. Calculate the system reliability of Design 2 to 3dp. c) Design 3: Assume the probability distribution of the time to failure of components is as follows. The probability distributions of component A is described by a a constant hazard rate with a mean life of 768 hrs. : [c] (1 mark) The probability distributions of component B is described by a Weibull distribution with shape parameter = 2.2 and characteristic life of 400 hours. The probability distribution of component C is described by a normal distribution with mean of 500 hours and standard deviation of 133 hours. Calculate the system reliability of Design 3 to 3dp. ANS: a) 0.837 b) 0.912 c) 0.854