Let X be the time of the first repair for a machine and let the hazard...
A computer repair shop has two work centers. The first center examines the computer to see what is wrong, and the second center repairs the computer. Let x1 and x2 be random variables representing the lengths of time in minutes to examine a computer (x1) and to repair a computer (x2). Assume x1 and x2 are independent random variables. Long-term history has shown the following times. Examine computer, x1: μ1 = 29.7 minutes; σ1 = 8.0 minutes Repair computer, x2:...
The amount of time taken by a machine repair person to repair a particular machine is a random variable with an exponential distribution with a mean of 1 hour. The repair persons employer pays the repair person a bonus of 2 whenever a repair takes less than 1/4 hours, and a bonus of 1 if the repair takes between 1/4 and 1/2 hours. Find the average bonus received per machine repaired (nearest) .1). A) .3 B) .4 C) .5 D)...
Q3. Each time a machine is repaired it remains "up" for an exponentially distributed time with rate A. It then fails and "down", and its failure is either of two types. If it is a type 1 failure, then the time to repair the machine is exponential with rate μ!, if it is a type 2 failure, then the repair time is exponential with rate H2. Each failure is, independently of the time it took the machine to fail, a...
Question: The time in months until a new bus must be brought into the repair center for service follows a Weibull law with cumulative hazard function. a) Calculate the hazard function lamda(t). Is this an aging or burn-in or constant hazard system?. Explain. b) Calculate the probability that a new bus will not require repair in the first 6 months. I am struggling with this question recently. I am quite lost at Weibull law. If possible, could you explain how...
. A facility of m identical machines is sharing a single repair person. The time to repair a failed machine is exponentially distributed with mean 1/λ. A machine, once operational, fails after a time that is exponentially distributed with mean 1/μ. All failure and repair times are independent. (a) Draw state transition diagram (b) Find out expression for the steady-state proportion of time where there is no operational machine.
1. Let X, X, and X represent the times necessary to perform successive repair tasks at a certain service facility. Suppose they are independent, normal random variables with expected values p4-14 t4-60 and ?_?? ?? 15. Consider the probability a. (10 pts. 2+ 3+2+3). Is the random variable T- X5 X2-.5x, normal? Why? Calculate its expectation and variance. DAT b. (6 pts.) Calculate the desired probability.
(1 point) Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameterA- 0.6. What is (a) the probability that a repair time exceeds 10 hours? (b) the conditional probability that a repair takes at least 11 hours, given that it takes more than 8 hours?
Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter λ=0.8, i.e., mean = 1/lambda. What is (a) the probability that a repair takes less than 77 hours?
4(25 points) Let X be a random variable with mean μ = E(X) and σ2 V(X). Let X = n Σ_1Xī be X2 + Xs) be the average of the the sample mean from a random sample (X X. Let X (X first three observations. (a) Prove that X is an unbiased estimator for μ. Prove that X is also an unbiased estimator for μ. (b) Explain that X is a consistent estimator for μ. Explain why X is not...
7 out of the first 9 problems and the problem 10. Show U owyou required to repair a machine is an exponential distributed random variable with parameter 2 1/2. What is a) The probability that a repair time exceeds 2 hours? b) The conditional probability that a repair takes at least 10 hours, given duration exceeds 9 hours? that its 7 out of the first 9 problems and the problem 10. Show U owyou required to repair a machine is...