CLO-3(C4) Let T be the lifetime of a device in hours (a) Find the reliability and...
[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
*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)
A device has an MTBF of 1,000 hours. a) Write the equation for its reliability as a function of time, R(t) = b) Plot the reliability from 0 – 5,000 hours in 100 hour increments
5. (10 points) let T-Weibull(a,B 3) be the lifetime of an electronic part. If n parts are put on test and the test is terminated after te hours, yielding r observed (ordered) failure times, t,,t, derive the formula for the MLE of a. 5. (10 points) let T-Weibull(a,B 3) be the lifetime of an electronic part. If n parts are put on test and the test is terminated after te hours, yielding r observed (ordered) failure times, t,,t, derive the...
Let X be the lifetime of a certain type of electronic device (measured in hours). The probability density function of X is f(x) =10/x^2 , x > c 0, x ≤ c (a) Find the value of c that makes f(x) a legitimate pdf of X. (b) Compute P(X < 20).
5.7 Seven pumps have failure times (in months) of 15.1, 10.7, 8.8, 11.3, 12.6, 14.4 and 8.7 Assume an exponential distribution. Assume the dataset is complete and all units have been operated to failure a) Find a point estimate of the MTTF b) Estimate the reliability of a pump for t 12 months c) Calculate the 95% two-sided confidence interval for λ, using the X2 distribution. Note: s,if the distribution is exponential, the 2T 2T distribution of the MTTF can...
please do them both for high rate Problem 3. Let X be a discrete random variable, with probability distribution P(X x)0.95, P(Xx2) 0.05 Determine X1 and X2 such that E[X] 0 and σ2(X)-7. Problem 4. The life X, in hours, of a certain device, has a pdf 100 x()t2 2 100 0, t<100 (a) What are the probability that this device will survive 150 hours of operation? (b) Find the life expectancy of the device.
2. A certain type of electronic component has a lifetime X (in hours) with probability density function given by otherwise. where θ 0. Let X1, . . . , Xn denote a simple random sample of n such electrical components. . Find an expression for the MLE of θ as a function of X1 Denote this MLE by θ ·Determine the expected value and variance of θ. » What is the MLE for the variance of X? Show that θ...
(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...
2- 5. The Weibull distribution has many applications in reliability engineering, survival analysis, and general insurance. Let B>0, 8>0. Consider the probability density function x>0 zero otherwise Recall (Homework #1) V-Χδ has an Exponential(8-T )-Gamma(u-l,e-1 ) distribution. Let X1, . , X/ be a random sample from the above probability distribution. y-ΣΧ.Σν i has a Gamma(u-n, θ- 1 ) distribution. !!! i-l 2. suppose δ is known. Let Xi, X2, , Xn be a random sample from the distribution with...