2) A system consists of four components connect as shown in the diagram for problem 35,...
A system consists of four components connected as shown in the following diagram: Assume A, B, C, and D function independently. If the probabilities that A, B, C, and D fail are 0.11, 0.05, 0.11, and 0.17, respectively, what is the probability that the system functions? Round the answer to four decimal places.
Civil Engineering System 34 A system consists of four components connected as shown in the following diagram: Assume A, B, C, and D function independently. If the probabilities that A, B, C, and D fail are 0.10, 0.05, 0.10, and 0.20, respectively, what is the probability that the system functions?
Question 4 [20 marks] A system consists of five components in two branches as shown in the following diagram: C-D-E- In other words, the system works if components A and B work or components C, D, and E work. Assume that the components fail independently with the following probabilities: P(A fails) = P(B fails) = 0.1 and P(C fails) = P(D fails) = P(E fails) = 0.2. (a) What is the probability that the system works? (b) Given that the...
Question 2 (6 points) A system contains two components, A and B, connected in series, as shown in the diagram. Assume A and B function independently. For the system to function, both components must function. a. If the probability that A fails is 0.05, and the probability that B fails is 0.03, b. If both A and B have probability p of failing, what must the value of pbe so c. If three components are connected in series, and each...
A system consists of four components. If more than two of the components fail, the system fails. If the components have an exponential time-to-fail distribution with a failure rate of 0.000388, what is the reliability of the system at time = 300?
3. Three components are connected to form a system as shown in the accompanying diagram. Because the compo- nents in the 2–3 subsystem are connected in parallel, that subsystem will function if at least one of the two individual components functions. For the entire system to function, component 1 must function and so must the 2–3 subsystem. 214 The experiment consists of determining the condition of each component [S (success) for a functioning compo- nent and F (failure) for a...
A system consists of five components is connected in series as shown below. -1 42 43 44 45 As soon as one component fails, the entire system will fail. Assume that the components fail independently of one another. (a) Suppose that each of the first two components have lifetimes that are exponentially distributed with mean 107 weeks, and that each of the last three components have lifetimes that are exponentially distributed with mean 136 weeks. Find the probability that the...
A system consists of three components A, B and C, which fails independently with probabilities 0.2, 03 and 0.2. Let X be the total number of failed components. (a) Find the probability distribution of X. (b) What is the probability that at least one component is working. (c) Find E(X^3 − 1). 3. (7 points) A system consists of three components A, B and C, which fails independently with probabilities 0.2, 03 and 0.2. Let X be the total number...
Problem 5. (11 points) The following circuit operates if and only if there is a path of functional devices from left to right. Assume devices fail independently and that the probability of failure of each device is as shown. What is the probability that the circuit does not operate? 0.02 0.01 0.01 0.01 0.01 0.02
1. If the probability that C fails is 0.1 and the probability that D fails is 0.12, find the probability that the system functions. Round the answer to four decimal places. 2. If both C and D have probability p of failing, what must the value of p be so that the probability that the system functions is 0.98? 3. If three components are connected in parallel, function independently, and each has probability p of failing, what must the value of...