A system of comprised of three independent components. The probability of failure for each component is given,
Homework Answers
Here we use theorem of conditional probability.
* given that Ai's are independent .
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A system of comprised of three independent components. The
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(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.
(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.
Part c (6) 6. A system comprised of three independent components. The probability of failure for...
Part c
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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...
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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,...
2 (20 polats) A lighting system is comprised of two lightbulbs work indepeedently. Manufacturer fested failure...
2 (20 polats) A lighting system is comprised of two lightbulbs work indepeedently. Manufacturer fested failure of these components and this failure is know n to oceur randomly with rate (.) of 0.5 per year (a) Define the lifetime random variable and its pdf function. What is the expected lifetime? What is the 80% (i.e., top 20%) lifetime years? (b) What is the probability that both lightbulbs are still functioning after 2 years? (Hint: calculate probability of one component functioning...
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...
I want help to solve this question A system is made up of three independent components....
I want help to solve this question
A system is made up of three independent components. It operates if at least two of the three components operate. If the reliability of each component is equal to 0.95, what is the reliability of the system?
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.
(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.
(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.
Part c
(6) 6. 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 #3 .3 a) Find the probability that the system works (A). b) Find the probability that at least one component works (B e) Find the probability that the system works, given that at least one component wor ks.
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2 (20 polats) A lighting system is comprised of two lightbulbs work indepeedently. Manufacturer fested failure of these components and this failure is know n to oceur randomly with rate (.) of 0.5 per year (a) Define the lifetime random variable and its pdf function. What is the expected lifetime? What is the 80% (i.e., top 20%) lifetime years? (b) What is the probability that both lightbulbs are still functioning after 2 years? (Hint: calculate probability of one component functioning...
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...
I want help to solve this question
A system is made up of three independent components. It operates if at least two of the three components operate. If the reliability of each component is equal to 0.95, what is the reliability of the system?
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