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Question #1 Failure distribution function for a given motor is shown below 10 (a) Derive and...
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)...
3. Given the survival function: S(t) exp(-t7) derive the probability density function and the hazard function...
3. Given the survival function: S(t) exp(-t7) derive the probability density function and the hazard function 4 Derive λ t f (t) S(t using the definition of the hazard function and basic definition of conditional probability. 5. Derive S(t) e-) using the definition of the hazard function. 6. Given the hazard function: derive the survival function and the probability density function 7. Prove that if T' has an arbitrary continuous distribution, the cumulative hazard of T, A(T), has an exponential...
1. Consider the multiplicative regression model for the failure time: t-e%+ßız x e, where o and a...
1. Consider the multiplicative regression model for the failure time: t-e%+ßız x e, where o and are unknown constants (parameters), r is a known, observed constant, and eexp(1) (a) Derive the probability density function of t. Do it directly, not the way it was done in the lecture (b) Using the formula sheet, write down the slides i. Expected value of t. ii. Median of t. ii. Survival function of t. (c) Give the hazard function of t. Show some...
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).
(1)The field test data in respect of 172 components is as given below. In the life-testing...
(1)The field test data in respect of 172 components is as given below. In the life-testing of 100 specimens of a particular device, the number of failures during each time interval of twenty hours is shown in Table below. Estimate and Plot: the hazard function, failure density and reliability function. Time/Hours Failure 0-1000 59 1000-2000 24 2000-3000 3000-4000 4000-5000 5000-6000 29 30 17 13 (1) calculate the reliability of the system shown in the figure below 0.8 5 0.8 0.9...
The time until failure for an electronic switch has an exponential distribution with an average time...
The time until failure for an electronic switch has an exponential distribution with an average time to failure of 4 years, so that λ = 1/4 = 0.25. (Round your answers to four decimal places.) (a)What is the probability that this type of switch fails before year 3? (b)What is the probability that this type of switch will fail after 5 years? (c) If two such switches are used in an appliance, what is the probability that neither switch fails...
. Suppose the time until failure (in years) of a laptop computer follows an exponential distribution...
. Suppose the time until failure (in years) of a laptop computer follows an exponential distribution with a mean life of 6 years. a) What is the median life of a laptop computer (in years)? b) What is the probability that a laptop computer will last more than 6 years?
6) Diagram of a probability density function is shown below. f(t) 5 6 7 10 11...
6) Diagram of a probability density function is shown below. f(t) 5 6 7 10 11 12 Time (hours) a. Derive the mathematical expression for the density function f(t). (6 marks) b. Find P (3<t<7) (3 marks)
6) Diagram of a probability density function is shown below. f(t) 5 6 7 10 11...
6) Diagram of a probability density function is shown below. f(t) 5 6 7 10 11 12 Time (hours) a. Derive the mathematical expression for the density function f(t). (6 marks) b. Find P (3<t<7) (3 marks)
6) Diagram of a probability density function is shown below. f(t) 7 5 10 11 12...
6) Diagram of a probability density function is shown below. f(t) 7 5 10 11 12 Time (hours) a. Derive the mathematical expression for the density function f(t). (6 marks) b. Find P (3<t<7). (3 marks)
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)...
3. Given the survival function: S(t) exp(-t7) derive the probability density function and the hazard function 4 Derive λ t f (t) S(t using the definition of the hazard function and basic definition of conditional probability. 5. Derive S(t) e-) using the definition of the hazard function. 6. Given the hazard function: derive the survival function and the probability density function 7. Prove that if T' has an arbitrary continuous distribution, the cumulative hazard of T, A(T), has an exponential...
1. Consider the multiplicative regression model for the failure time: t-e%+ßız x e, where o and are unknown constants (parameters), r is a known, observed constant, and eexp(1) (a) Derive the probability density function of t. Do it directly, not the way it was done in the lecture (b) Using the formula sheet, write down the slides i. Expected value of t. ii. Median of t. ii. Survival function of t. (c) Give the hazard function of t. Show some...
(1)The field test data in respect of 172 components is as given below. In the life-testing of 100 specimens of a particular device, the number of failures during each time interval of twenty hours is shown in Table below. Estimate and Plot: the hazard function, failure density and reliability function. Time/Hours Failure 0-1000 59 1000-2000 24 2000-3000 3000-4000 4000-5000 5000-6000 29 30 17 13 (1) calculate the reliability of the system shown in the figure below 0.8 5 0.8 0.9...
6) Diagram of a probability density function is shown below. f(t) 5 6 7 10 11 12 Time (hours) a. Derive the mathematical expression for the density function f(t). (6 marks) b. Find P (3<t<7) (3 marks)
6) Diagram of a probability density function is shown below. f(t) 5 6 7 10 11 12 Time (hours) a. Derive the mathematical expression for the density function f(t). (6 marks) b. Find P (3<t<7) (3 marks)
6) Diagram of a probability density function is shown below. f(t) 7 5 10 11 12 Time (hours) a. Derive the mathematical expression for the density function f(t). (6 marks) b. Find P (3<t<7). (3 marks)
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