1. The failure rate function of an item is z ( t ) = t^-1/2. Derive:...
1. The failure rate function of an item is z ( t ) = t^-1/2. Derive: The mean time to failure.
2. A component with time to failure T has failure rate
function
z ( t ) = kt fort > 0 and k > 0. Determine the probability
that a component which is functioning after 200 hours is still
functioning after 400 hours, when k = 2.*10^-6 (hours).
Homework Answers
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1. The failure rate function of an item is z ( t ) = t^-1/2.
Derive:...
Question #2 The probability density function of the time to failure of a component is described...
Question #2 The probability density function of the time to failure of a component is described by the following equation where k is constant (t) kt,t is in year) elsewhere (a) Find the k value (b) Find MTTF (c) Find the failure rate function (d) Graph the failure rate function and draw a conclusion
Problem 2 Fct) (a) Derive and sketch the failure density function (3 marks) (b) Derive and...
Problem 2 Fct) (a) Derive and sketch the failure density function (3 marks) (b) Derive and sketch the and sketch the reliability function (3 marks) (c) Derive and sketch the hazard rate function (3 marks) (d) Would you recommend a burn in period for this motor, why or why not? (3 marks) (e) What is the probability a new motor will last more than 2 years? (3 marks) (f) Determine the mean time to fail for the motor. (3 marks)...
Question #1 Failure distribution function for a given motor is shown below 10 (a) Derive and...
Question #1 Failure distribution function for a given motor is shown below 10 (a) Derive and sketch the failure density function (8 marks) b) Derive and sketch the and sketch the reliability function (6 marks) (c) Derive and sketch the hazard rate function (6 marks) (d) Would you recommend a burn in period for this motor, why or why not? (4 marks) (e) What is the probability a new molor will last more than 2 years? (4 marks) Determine the...
2.27 The time to failure T of a component is assumed to be uniformly distributed over...
2.27 The time to failure T of a component is assumed to be uniformly distributed over (a, b. The probability density is thus (1)for a<isb b-a Derive the corresponding survivor function R(t) and failure rate function z(). Draw a sketch of z()
The time to failure T of a component is assumed to be uniformly distributed over (a,...
The time to failure T of a component is assumed to be uniformly distributed over (a, b]. The probability density is thus for a<t< b Derive the corresponding survivor function R(t) and failure rate function z(t). Draw a sketch of z(t).
The time to failure T of a component has probability density f ( t ) as...
The time to failure T of a component has probability density f (
t ) as shown
(b) Derive the corresponding survivor function R ( t ) .
(c) Derive the corresponding failure rate function z ( t ) , and
make a sketch of z(t)
Note: The f(t) is a valid pdf (so we can obtain c or the height
of the triangle). Information are enough to solve this problem.
f(t) a -b a b Time t Fig. 2.27...
ne 10. 2019 4. A random process Z(t) is given by, Z(t) = Kt, where K...
ne 10. 2019 4. A random process Z(t) is given by, Z(t) = Kt, where K is a random variable The probability dessity function for K is given below. Use this information to answer the questions below (20 points k <-1 0 fK(k)=-k-1sks k> 1 0 (a) Find the mean function for Z(t). (b) Find the autocovariance function for Z(e). (c) Is this process wide sense stationary (WSS)? Explain your answer in 2-3 sentences.
ne 10. 2019 4. A random...
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...
Please answer all the questions thank you ne 10. 2019 4. A random process Z(t) is...
Please answer all the questions thank you
ne 10. 2019 4. A random process Z(t) is given by, Z(t) = Kt, where K is a random variable The probability dessity function for K is given below. Use this information to answer the questions below (20 points k <-1 0 fK(k)=-k-1sks k> 1 0 (a) Find the mean function for Z(t). (b) Find the autocovariance function for Z(e). (c) Is this process wide sense stationary (WSS)? Explain your answer in 2-3...
*Suppose a device has a constant failure rate of r(t)-A, the PDF of its lifetime follows an expon...
*Suppose a device has a constant failure rate of r(t)-A, the PDF of its lifetime follows an exponential 1. determine the reliability function, R(t) 2. determine the device's mean-time-to-fail (MTTF)
*Suppose a device has a constant failure rate of r(t)-A, the PDF of its lifetime follows an exponential 1. determine the reliability function, R(t) 2. determine the device's mean-time-to-fail (MTTF)
Question #2 The probability density function of the time to failure of a component is described by the following equation where k is constant (t) kt,t is in year) elsewhere (a) Find the k value (b) Find MTTF (c) Find the failure rate function (d) Graph the failure rate function and draw a conclusion
Problem 2 Fct) (a) Derive and sketch the failure density function (3 marks) (b) Derive and sketch the and sketch the reliability function (3 marks) (c) Derive and sketch the hazard rate function (3 marks) (d) Would you recommend a burn in period for this motor, why or why not? (3 marks) (e) What is the probability a new motor will last more than 2 years? (3 marks) (f) Determine the mean time to fail for the motor. (3 marks)...
Question #1 Failure distribution function for a given motor is shown below 10 (a) Derive and sketch the failure density function (8 marks) b) Derive and sketch the and sketch the reliability function (6 marks) (c) Derive and sketch the hazard rate function (6 marks) (d) Would you recommend a burn in period for this motor, why or why not? (4 marks) (e) What is the probability a new molor will last more than 2 years? (4 marks) Determine the...
2.27 The time to failure T of a component is assumed to be uniformly distributed over (a, b. The probability density is thus (1)for a<isb b-a Derive the corresponding survivor function R(t) and failure rate function z(). Draw a sketch of z()
The time to failure T of a component is assumed to be uniformly distributed over (a, b]. The probability density is thus for a<t< b Derive the corresponding survivor function R(t) and failure rate function z(t). Draw a sketch of z(t).
The time to failure T of a component has probability density f (
t ) as shown
(b) Derive the corresponding survivor function R ( t ) .
(c) Derive the corresponding failure rate function z ( t ) , and
make a sketch of z(t)
Note: The f(t) is a valid pdf (so we can obtain c or the height
of the triangle). Information are enough to solve this problem.
f(t) a -b a b Time t Fig. 2.27...
ne 10. 2019 4. A random process Z(t) is given by, Z(t) = Kt, where K is a random variable The probability dessity function for K is given below. Use this information to answer the questions below (20 points k <-1 0 fK(k)=-k-1sks k> 1 0 (a) Find the mean function for Z(t). (b) Find the autocovariance function for Z(e). (c) Is this process wide sense stationary (WSS)? Explain your answer in 2-3 sentences.
ne 10. 2019 4. A random...
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...
Please answer all the questions thank you
ne 10. 2019 4. A random process Z(t) is given by, Z(t) = Kt, where K is a random variable The probability dessity function for K is given below. Use this information to answer the questions below (20 points k <-1 0 fK(k)=-k-1sks k> 1 0 (a) Find the mean function for Z(t). (b) Find the autocovariance function for Z(e). (c) Is this process wide sense stationary (WSS)? Explain your answer in 2-3...
*Suppose a device has a constant failure rate of r(t)-A, the PDF of its lifetime follows an exponential 1. determine the reliability function, R(t) 2. determine the device's mean-time-to-fail (MTTF)
*Suppose a device has a constant failure rate of r(t)-A, the PDF of its lifetime follows an exponential 1. determine the reliability function, R(t) 2. determine the device's mean-time-to-fail (MTTF)
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