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Cycle availability of a system. In the jargon of system maintenance, “cycle availability" is defined as the proba- bility that a system is functioning at any point in time. The U.S. Department of Defense developed a series of per- formance measures for assessing system cycle availability (START, Vol. 11, 2004). Under certain assumptions about the failure time and maintenance time of a system, cycle 66 availability is shown to be uniformly distributed between 0 and 1. Find the following parameters for cycle availability: mean, standard deviation, 10th percentile, lower quartile, and upper quartile. Interpret the results.

Cycle availability of a system. In the jargon of system maintenance, “cycle availability" is defined as the proba- bility that a system is functioning at any point in time. The U.S. Department of Defense developed a series of per- formance measures for assessing system cycle availability (START, Vol. 11, 2004). Under certain assumptions about the failure time and maintenance time of a system, cycle 66 availability is shown to be uniformly distributed between 0 and 1. Find the following parameters for cycle availability: mean, standard deviation, 10th percentile, lower quartile, and upper quartile. Interpret the results.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Transcription for Educational Website: **Load on Timber Beams** Timber beams are widely used in home construction. When the load (measured in pounds) per unit length has a constant value over part of a beam, the load is said to be uniformly distributed over that part of the beam. Uniformly distributed beam loads were used to derive the stiffness distribution of the beam in the *American Institute of Aeronautics and Astronautics Journal* (May 2013). Consider a cantilever beam with a uniformly distributed load between 100 and 115 pounds per linear foot. a. What is the probability that a beam load exceeds 110 pounds per linear foot? b. What is the probability that a beam load is less than 102 pounds per linear foot? c. Find a value \( L \) such that the probability the beam load exceeds \( L \) is only 0.1. --- **Cycle Availability of a System** In the jargon of system maintenance, “cycle availability” is defined as the probability that a system is functioning at any point in time. The U.S. Department of Defense developed a series of performance measures for assessing system cycle availability (*START*, Vol. 11, 2004). Under certain assumptions about the failure time and maintenance time of a system, cycle availability is shown to be uniformly distributed between 0 and 1. Find the following parameters for cycle availability: mean, standard deviation, 10th percentile, lower quartile, and upper quartile. Interpret the results. --- **Soft-Drink Dispenser** The manager of a local soft-drink bottling company believes that when a new beverage-dispensing machine is set to dispense 7 ounces, it in fact dispenses an amount \( x \) at random anywhere between 6.5 and 7.5 ounces, inclusive. Suppose \( x \) has a uniform probability distribution. a. Is the amount dispensed by the beverage machine a discrete or a continuous random variable? Explain. b. Graph the frequency function for \( x \), the amount of beverage dispensed by the machine. Label the axes.
Transcribed Image Text:Transcription for Educational Website: **Load on Timber Beams** Timber beams are widely used in home construction. When the load (measured in pounds) per unit length has a constant value over part of a beam, the load is said to be uniformly distributed over that part of the beam. Uniformly distributed beam loads were used to derive the stiffness distribution of the beam in the *American Institute of Aeronautics and Astronautics Journal* (May 2013). Consider a cantilever beam with a uniformly distributed load between 100 and 115 pounds per linear foot. a. What is the probability that a beam load exceeds 110 pounds per linear foot? b. What is the probability that a beam load is less than 102 pounds per linear foot? c. Find a value \( L \) such that the probability the beam load exceeds \( L \) is only 0.1. --- **Cycle Availability of a System** In the jargon of system maintenance, “cycle availability” is defined as the probability that a system is functioning at any point in time. The U.S. Department of Defense developed a series of performance measures for assessing system cycle availability (*START*, Vol. 11, 2004). Under certain assumptions about the failure time and maintenance time of a system, cycle availability is shown to be uniformly distributed between 0 and 1. Find the following parameters for cycle availability: mean, standard deviation, 10th percentile, lower quartile, and upper quartile. Interpret the results. --- **Soft-Drink Dispenser** The manager of a local soft-drink bottling company believes that when a new beverage-dispensing machine is set to dispense 7 ounces, it in fact dispenses an amount \( x \) at random anywhere between 6.5 and 7.5 ounces, inclusive. Suppose \( x \) has a uniform probability distribution. a. Is the amount dispensed by the beverage machine a discrete or a continuous random variable? Explain. b. Graph the frequency function for \( x \), the amount of beverage dispensed by the machine. Label the axes.
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