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Part c (6) 6. A system comprised of three independent components. The probability of failure for...
(5) 5. A system comprised of three independent components. The probability of failure for each component...
(5) 5. A system comprised of three independent components. The probability of failure for each component is given. (Use our standard notation: Ai, i 1,2,3; A.) #1 .1 #2 .2 #3 .3 a) Find the probability that the system works - [A]. b) Find the probability that exactly one component works B c) Find the probability that at least one component works [C.
(6) 3. A system comprised of three independent components. The probability of failure for each component...
(6) 3. A system comprised of three independent components. The probability of failure for each component is given. #2 .2 #3.3 # 1 .1 A2,A3,A Use our standard Notation: Ali (system operates properly} a) Find the probability that the system operates properly. b) Find the probability that at most two of the components work. (event B) c) Find the probability that the system operates properly if at most two of the components work.
A system of comprised of three independent components. The probability of failure for each component is...
A system of comprised of three independent components. The
probability of failure for each component is given,
D4 MORE NON-CAR (6) 3. A system comprised of thrce independent components. The probability of failure for each component is given. #2.2 #3.3 #1 .1 Use our standard Noration: A,, A2, A3, A [system operates properly) a) Find the probability that the system operates properly. b) Find the probability that at most two of the components work. (event B) c) Find the probability...
2, (20%) A particular operation has six components. Each component has a failure probability q, independent of any othe...
2, (20%) A particular operation has six components. Each component has a failure probability q, independent of any other component. The operation is successful if both of the following conditions hold: Component 1, 2, and 3 all work, or component 4 works. Either component 5 or component 6 works. The block diagram of this operation is shown below. b. (10%) Suppose we can replace one of the components with a more reliable component that has failure probability of q/2 Which...
Problem 4 Consider the system of components connected as depicted below. The system can be thought...
Problem 4 Consider the system of components connected as depicted below. The system can be thought of as being comprised of two subsystems: one with components A and B, and the other with components C and D. Components A and B are connected in parallel, therefore that subsystem works iff either A or B works. Since C and D are connected in series, that subsystem works iff both C and D work. Components work independent of each other (that is,...
A parallel system consisting of 4 independent components works if at least one component works. However,...
A parallel system consisting of 4 independent components works if at least one component works. However, a seriesl system consisting of 4 independent components works if all components work. Now suppose probability p of any component works is 0.5. Compute the following quantity and interpret your results.
A system consists of three components A, B and C, which fails independently with probabilities 0.2,...
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...
(12 points) Consider the system comprised of three components as shown below. Suppose The lifetime of...
(12 points) Consider the system comprised of three components as shown below. Suppose The lifetime of Component 1 is exponentially-distributed with parameter 11 = 1/10. • The lifetime of Component 2 is exponentially-distributed with parameter 12 = 1/20. • The lifetime of Component 3 is exponentially-distributed with parameter 13 = 1/15. The system is working if both (A) Component 1 is working, and (B) Component 2 or/and Component 3 is working. Compute the probability that the system is still working...
An aircraft system is modeled as being comprised of (3) independent subsystems - each critical -...
An aircraft system is modeled as being comprised of (3) independent subsystems - each critical - with reliability as follows : – Electrical => 15% probability of failure – Mechanical/Hydraulic => 10% probability of failure – Fuel/Powerplant => 5% probability of failure Question 1: What is the overall reliability of the aircraft system? Two identical Electrical subsystems are installed side-by-side in a hot-swap backup configuration. Question 2: Assuming all independent subsystem components have the same reliability as previously stated, what...
4. A system consists of three independent components connected in perallol (i.e., the system is operational...
4. A system consists of three independent components connected in perallol (i.e., the system is operational if at least one component is operational). The status of each component is checked at the beginning of every day. An opcrational component will break down at the end of a day with probability 02.Its repir takes the entire next day after which the component becomes operational again. The daily cost of lost production due to non-working components is k, where k is the...
(5) 5. A system comprised of three independent components. The probability of failure for each component is given. (Use our standard notation: Ai, i 1,2,3; A.) #1 .1 #2 .2 #3 .3 a) Find the probability that the system works - [A]. b) Find the probability that exactly one component works B c) Find the probability that at least one component works [C.
(6) 3. A system comprised of three independent components. The probability of failure for each component is given. #2 .2 #3.3 # 1 .1 A2,A3,A Use our standard Notation: Ali (system operates properly} a) Find the probability that the system operates properly. b) Find the probability that at most two of the components work. (event B) c) Find the probability that the system operates properly if at most two of the components work.
A system of comprised of three independent components. The
probability of failure for each component is given,
D4 MORE NON-CAR (6) 3. A system comprised of thrce independent components. The probability of failure for each component is given. #2.2 #3.3 #1 .1 Use our standard Noration: A,, A2, A3, A [system operates properly) a) Find the probability that the system operates properly. b) Find the probability that at most two of the components work. (event B) c) Find the probability...
2, (20%) A particular operation has six components. Each component has a failure probability q, independent of any other component. The operation is successful if both of the following conditions hold: Component 1, 2, and 3 all work, or component 4 works. Either component 5 or component 6 works. The block diagram of this operation is shown below. b. (10%) Suppose we can replace one of the components with a more reliable component that has failure probability of q/2 Which...
Problem 4 Consider the system of components connected as depicted below. The system can be thought of as being comprised of two subsystems: one with components A and B, and the other with components C and D. Components A and B are connected in parallel, therefore that subsystem works iff either A or B works. Since C and D are connected in series, that subsystem works iff both C and D work. Components work independent of each other (that is,...
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...
(12 points) Consider the system comprised of three components as shown below. Suppose The lifetime of Component 1 is exponentially-distributed with parameter 11 = 1/10. • The lifetime of Component 2 is exponentially-distributed with parameter 12 = 1/20. • The lifetime of Component 3 is exponentially-distributed with parameter 13 = 1/15. The system is working if both (A) Component 1 is working, and (B) Component 2 or/and Component 3 is working. Compute the probability that the system is still working...
4. A system consists of three independent components connected in perallol (i.e., the system is operational if at least one component is operational). The status of each component is checked at the beginning of every day. An opcrational component will break down at the end of a day with probability 02.Its repir takes the entire next day after which the component becomes operational again. The daily cost of lost production due to non-working components is k, where k is the...
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