The time to failure (in hours) of a piece of equipment is uniformly distributedover (0, 1000) hours.(a) Determine the MTTF.(b) Determine the MTTF if preventive maintenance will restore the system toas good as new condition and is performed every 100 operating hours.(c)Compare the reliability with and without preventive maintenance at 225operating hours. Assume the 100 hour maintenance interval and amaintenance-induced failure probability of 0.01 each time preventivemaintenance is performed.

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Answered: The time to failure (in hours) of a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider a population (or more precisely a population density) of size N in a small city in the former Soviet Union, which is completely susceptible to a rare disease known as Suriv-Sugob-A, named after a Russian admiral who was the first to contract the disease after an encounter with indigenous people in the Siberian rain forest. The disease is transmitted by droplets through the air or direct contact. It has a transmission coefficient of ?, which is the probability of successful transmission once a susceptible individual is exposed. The corresponding recovery period is 1/? days. Suppose you are in charge of managing an immunization campaign to protect against an outbreak of Suriv[1]Sugob-A. Assume the following disease characteristics: ? = 1 ×10-6 , ? = .25, and a population of N = 750,000. Please Answer (A) (a) determine the length of the outbreak if your entire population is susceptible.
A computer system queues up batch jobs and processes them on an FCFS basis.Between 2 and 5 P.M., jobs arrive at an average rate of 30 per hour and require anaverage of 1.2 minutes of computer time. Assume the arrival process is Poissonand the processing times are exponentially distributed. b. Using a normal approximation of the flow time distribution for the LCFS andrandom cases, estimate the probability that the flow time in the system exceeds10 minutes in each case.
The desired seeding rate of a farmer on his corn field is 90,000 seeds per hectare. If emergence of 90% is expected, what should be expected plant population?
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An insurance company supposes that each person has an accident parameter and that the yearly number of accidents of someone whose accident parameter is λ is Poisson distributed with mean λ. They also suppose that the parameter value of a newly insured person can be assumed to be the value of a gamma random variable with parameters s and α. (a) If a newly insured person has n accidents in her first year, find the conditional density of her accident parameter. (b) Also, determine the expected number of accidents that she will have in the following year.
The owner of an automobile insures it against damage by purchasing an insurance policy with a deductible of 250. In the event that the automobile is damaged, repair costs can be modeled by a uniform random variable on the interval [0, 1500]. Determine the standard deviation of the insurance payment in the event that the automobile is damaged
A die is weighted such that an even number is twice as likely to come out as an odd number. If the die is rolled twice and Y is the absolute difference between the two numbers that turn up, construct the probability mass function of Y and compute its variance.
Suppose an electric-vehicle manufacturing company estimates that a driver who commutes 50 miles per day in a particular vehicle will require a nightly charge time of around 1 hour and 30 minutes (90 minutes) to recharge the vehicle's battery. Assume that the actual recharging time required is uniformly distributed between 70 and 110 minutes. What is the probability that the recharge time will be less than 101 minutes?(Enter your answer with three decimal places).
The time to fly between New York City and Chicago is uniformly distributed with a minimum of 56 minutes and a maximum of 100 minutes. What is the probability that a flight is less than 63 minutes?
A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1,300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with σ = 61. Let μ denote the true average compressive strength. For a test with α = 0.01, what is the probability that the mixture will be judged unsatisfactory when in fact μ = 1,350 (a type II error)? (Round your answer to four decimal places.)
A soft-drink machine at a steak house is regulated so that the amount of drink dispensed is approximately normally distributed with a mean of 210 milliliters and a standard deviation of 12 milliliters. The machine is checked periodically by taking a sample of 16 drinks and computing the average content. If x falls in the interval 201<x<219, the machine is thought to be operating satisfactorily; otherwise, the owner concludes that μ≠210 milliliters. Find the probability of committing a type II error when μ=198 milliliters.

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