here for above to be valid: f(t) dt =1
f(t) dt = Cte-t/2 dt =-C*(2te-t/2-4e-t/2)|0 =4C =1
therefore C =1/4
hence P(system last for at least 5 hours) =P(T>5)
= f(t) dt = (1/4)te-t/2 dt =-(1/4)*(2te-t/2-4e-t/2)|5 =0.2873
The lifetime T in hours of a system (with some redundancy) has pdf fr(t) Cte 110)(t)....
The lifetime T in hours of a system (with some redundancy) has pdf What is the probability that the system will last for at least 5 hours?
[25] Question No 03: The lifetime T of a device has pdf given by: s2e-2 (2e-2(t-Tot >T. fr(t)= Ot<T. a) Find the reliability and MTTF of the device b) Find the failure rate function c) How many hours of operation can be considered to achieve 98% reliability
CLO-3(C4) Let T be the lifetime of a device in hours (a) Find the reliability and MTTF fr(t) = 5/t2 t> 5 0t5 (b) Find the failure rate function r(t). (c) How many hours of operation can be considered to achieve 95% reliability CLO-3(C4) Let T be the lifetime of a device in hours (a) Find the reliability and MTTF fr(t) = 5/t2 t> 5 0t5 (b) Find the failure rate function r(t). (c) How many hours of operation can...
The lifetime X in hours of a certain electrical component has the pdf If a random sample of 36 is taken from these components, find P(3 + 100 < 111) We were unable to transcribe this imageWe were unable to transcribe this image
3. Let and be independent random variables representing the lifetime (in 100 hours) of Type A and Type B light bulbs, respectively. Both variables have exponential distributions, and the mean of X is 2 and the mean of Y is 3. a) Find the joint pdf f(x, y) of X and Y. b) Find the conditional pdf fa(ylx) of Y given Xx. c) Find the probability that a Type A bulb lasts at least 300 hours and a Type B...
A system has m controllers and n actuators. The system has redundancy built in so that it will be operational if at least one controller and two actuators have not failed. All controllers and actuators fail independently. If the probability that a controller fails is pc = 0.25, and the probability that an actuator fails is pa = 0.1, find the probability that the system will be operational for: (a) 1 controller, 2 actuators (b) 2 controllers, 2 actuators (c)...
*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)
3. The cumulative distribution function (CDF), of a particular brand of flash drive is Fr(t) 0 for t s5.0, Fr(t) (t-5.0) for 5.0<ts6.0, and Fr(t) 1 for t> 6.0. Here, time t has the units of years. a. Sketch Fr(t) versus t. Show proper axis labels, scales, and units. b. Express mathematically reliability RT(t) versus t for t2 0, and sketch it below Fr(t) to the same horizontal scale. Show proper axis labels, scales, and units. Express mathematically probability density...
The lifetime of a device (in hours) has the Gam(4,0.01) distribution. a) Find the probability that the device will last more than 300 hurs. b) what is the 90th percentile of this distribution?
The lifetime of a microprocessor is exponentially distributed with a variance of 4,000,000 hours. a. What proportion of microprocessors will function for less than 5,000 hours? b. A microprocessor has been functioning for 1,000 hours. What is the probability that it will function for a total of at least 6,000 hours?