The probability density function of the time to failure of an electronic component in a copier...
The probability density function of the time to failure of an
electronic component in a copier (in hours) is
for
. Determine the probability that
a) A component lasts more than 3000 hours before failure.
b) A component fails in the interval from 1000 to 2000 hours.
c) A component fails before 1000 hours.
d) Determine the number of hours at which 10% of all components
have failed.
Homework Answers
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The probability density function of the time to failure of an
electronic component in a copier...
4. The amount of time T (in hours) that a certain electrical component takes to fail...
4. The amount of time T (in hours) that a certain electrical component takes to fail has an exponential distribution with parameter > 0. The component is found to be working at midnight on a certain day. Let N be the number of full days after this time before the component fails (so if the component fails before midnight the next day, N = 0). (a) What is the probability that the component lasts at least 24 hours? (b) Find...
In a reliability context a randomly selected electronic component will undergo an accelerated failure time test....
In a reliability context a randomly selected electronic component will undergo an accelerated failure time test. Let X take the value 1 if the component lasts less than 50 hours and zero otherwise, and Y take the value 1 if the component lasts between 50 and 90 hours and zero otherwise. The probabilities that a randomly selected component will last less than 50 hours, between 50 and 90 hours, and more than 90 hours are 0.2, 0.5, and 0.3. Find...
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
4.5. There are two common types of failure to a critical electronic element of some machinery:...
4.5. There are two common types of failure to a critical electronic element of some machinery: either component A or component B may fail. If either component fails, the machinery goes down. Component A fails according to a Poisson process with mean rate 1.1 failures per shift. (The company operates 24/7 using eight-hour shifts.) Component B fails according to a Poisson process with a mean rate of 1.2 failures per day (a) What is the probability that there will be...
7 - 22 (page 365). Spacescope Inc. has an electronic component that has a failure rate...
7 - 22 (page 365). Spacescope Inc. has an electronic component that has a failure rate of 0.0000165 units/hour. Find the mean time to failure (MTTF). What is the probability (assume an exponential distribution) that the component wil not have failed after 15,000 hours of operation? Calculate your answer using the appropriate mathematical formula, and verify your results using Excel.
- (a) The failure time is 15 points) opns below PDF years (x) of a component...
- (a) The failure time is 15 points) opns below PDF years (x) of a component has the probabilsty density function ce o elsewer Find the probability that the component will fail in the first 2 years P( x S 2) (b) A system includes four components (A, B, and C), one of which will fail overa time period. The probabilities of the mutually exclusive component failures are P(C)-0.25 P(D) 0.10 P(A) 0.20 P(B) 0.15 The probability ofa system failure...
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...
Interest centers around the life of an electronic component. Suppose it is known that the probability...
Interest centers around the life of an electronic component. Suppose it is known that the probability that the component survives for more than 7000 hours is 0.49 Suppose also that the probability that the component survives no longer than 2000 hours is 0.04 (a) What is the probability that the life of the component is less than or equal to 7000 hours? (b) What is the probability that the life is greater than 2000 hours?
You are given the following probability density function, 6x(r), for the cosine of the surface an...
You are given the following probability density function, 6x(r), for the cosine of the surface angle, S, of a laser etching tool. The distribution function has one parameter, a, and one constant, c. -1sxs1 a) What is the value of the constant, e? b) What is the moment estimator for a? c) Explain how you can determine if this moment estimator is unbiased. t... . 24) denote a random sample of sample size n 24 with sample mean of-0.01 and...
(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...
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
4.5. There are two common types of failure to a critical electronic element of some machinery: either component A or component B may fail. If either component fails, the machinery goes down. Component A fails according to a Poisson process with mean rate 1.1 failures per shift. (The company operates 24/7 using eight-hour shifts.) Component B fails according to a Poisson process with a mean rate of 1.2 failures per day (a) What is the probability that there will be...
7 - 22 (page 365). Spacescope Inc. has an electronic component that has a failure rate of 0.0000165 units/hour. Find the mean time to failure (MTTF). What is the probability (assume an exponential distribution) that the component wil not have failed after 15,000 hours of operation? Calculate your answer using the appropriate mathematical formula, and verify your results using Excel.
- (a) The failure time is 15 points) opns below PDF years (x) of a component has the probabilsty density function ce o elsewer Find the probability that the component will fail in the first 2 years P( x S 2) (b) A system includes four components (A, B, and C), one of which will fail overa time period. The probabilities of the mutually exclusive component failures are P(C)-0.25 P(D) 0.10 P(A) 0.20 P(B) 0.15 The probability ofa system failure...
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...
You are given the following probability density function, 6x(r), for the cosine of the surface angle, S, of a laser etching tool. The distribution function has one parameter, a, and one constant, c. -1sxs1 a) What is the value of the constant, e? b) What is the moment estimator for a? c) Explain how you can determine if this moment estimator is unbiased. t... . 24) denote a random sample of sample size n 24 with sample mean of-0.01 and...
(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...
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