The system sketched below is used to regulate the downstream pressure of gas in a chemical plant. There are two regulators whose function is to keep the downstream pressure at a constant value. The upstream pressure fluctuates, but is always much higher than the required downstream pressure. The regulators function independently, but both sense the downstream pressure at the same point (X) High presure Low presure A regulator can fail in one of two ways: 'open', in which case it becomes 'straight through' so that the flow of gas is unrestricted, and reliability in this mode is RO; or 'closed, in which it totally blocks the flow of gas and reliability in this mode is Rc a. On the assumption that the two types of failure are independent, produce expressions for system reliability () for the system failing due to total loss of flow; () for the system failing due to overpressure downstream. b. The times to failure of the regulators are described by the following distributions: Closed-exponential with mean life 2 years Open - Weibull with p-1.8 and n-1.6 years What are the probabilities of the system giving one year of failure-free operation in each mode? C. What is the probability of obtaining one year of failure-free operation irrespective of the mode of failure?