A floor cleaning robot contains 4 modules that are critical to its operation.The modules and their individual reliabilities are listed below.Movement module0.98Data Storage Module0.999Learning Module0.99Vision Module0.94What is the probability that the system will be up and running?Suppose this number is too low and it is desired to improve the reliabilitythrough redundant elements.What would be the new reliability from each one of these changes?a. back up the Vision module with an identical module.b. back up the movement module with an identical module, but not the vision module.

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Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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At DataTech Solutions, the reliability of their server systems is a critical factor in maintaining smooth operations. The company knows that the probability of a server experiencing no downtime due to technical issues is 0.95. When a server is functioning smoothly, there is a 0.9 probability that the network performance is also optimal. However, if a server encounters technical problems, the probability of having optimal network performance drops to 0.3. A server is chosen at random for assessment, and its network performance is found to be optimal. What is the updated probability that the server is running without any technical issues?
One of the industrial robots designed by a leading producer of servomechanisms has four major components. Components’ reliabilities are .98, .95, .94, and .90. All of the components must function in order for the robot to operate effectively.a. Compute the reliability of the robot.b. Designers want to improve the reliability by adding a backup component. Due to space limitations, only one backup can be added. The backup for any component will have the same reliability as the unit for which it is the backup. Which component should get the backup in orderto achieve the highest reliability?c. If one backup with a reliability of .92 can be added to any one of the main components, which component should get it to obtain the highest overall reliability?
A typical retail transaction consists of several smaller steps, which can be considered components subject to failure. A list of such components might include: Let the eight probabilities of success be .92, .94, .99, .99, .98, .97,.95, and .96. What is the reliability of the system; that is, the probabilitythat there will be a satisfied customer? If you were the storemanager, what do you think should be an acceptable value forthis probability? Which components would be good candidatesfor backup, which for redesign?
One of the industrial robots designed by a leading producer of servomechanisms has four major components. Component 0.98, 0.95, 0.94, and 0.90. All of the components must function in order for the robot to operate effectively. b. Designers want to improve the reliability by adding a backup component. Due to space limitations, only one backup cbackup for any component will have the same reliability as the unit for which it is the backup. Compute the reliability of the robot.
Assume that a computer has two 1TB disks, D0 and D1. The Mean Time to Failure (MTTF) ofeach disk is 1M hours.a. If the disk system is configured to have 2TB total storage capacity, when any of the two disksfails, the disk system fails. What is the MTTF of the disk system?b. Mirroring (RAID-1) is a technique can improve the reliability of disk systems by usingredundancy. Each data block will have two identical copies stored in both D0 and D1. Under thisconfiguration, the disk system has only 1TB total storage capacity; but it only fails when bothdisks fail (e.g. when the failed disk is being repaired, the second disk also fails). If the MTTR of afailed disk is 20 hours, what is the MTTF of the disk system now?
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The failure rate of an electronic system is 0.005 failures per hour and its time to failure can be modelled by an exponential distribution and the system will fail 50 hours mission,Calculate:(a)The reliability of the system. [10 Marks](b) The cumulative distribution function of the system. PLEASE ANSWER ALL
CAN YOU PROVIDE THIS IN EXCEL, I CANT FIGURE OUT HOW TO DO THE EQUATIONS IN EXCEL. One of the industrial robots designed by a leading producer of servomechanisms has four major components. Components’ reliabilities are .98, .95, .94, and .90. All of the components must function in order for the robot to operate effectively.a. Compute the reliability of the robot.b. Designers want to improve the reliability by adding a backup component. Due to space limitations, only one backup can be added. The backup for any component will have the same reliability as the unit for which it is the backup. Which component should get the backup in orderto achieve the highest reliability?c. If one backup with a reliability of .92 can be added to any one of the main components, which component should get it to obtain the highest overall reliability?
In designing a new space vehicle, NASA needs to decide whether to provide 0, 1 or 2 backup systems for a critical component of the vehicle. The first backup system, if included, comes into use only if the original system fails. The second backup system, if included, comes into use only if the original system and the first backup system both fail. NASA engineers claim that each system, independent of the others, has a 1.5% chance of failing if called into use. Each backup system costs $70,000 to produce and install within the vehicle. Once the vehicle is in flight, the mission will be scrubbed (ended early) only if the original system and all backups fail. The cost of a scrubbed mission, in addition to production costs, is assessed to be $5,000,000. How many backup systems are needed to minimize NASA’s expected total cost?
The reliability of a system with n independent components equals:a) the sum of the individual reliabilities.b) the minimum reliability among all components.c) the maximum reliability among all components.d) the product of the individual reliabilities.e) the average of the individual reliabilities.
A jet engine has 10 components in series. Th e average reliabilityof each component is 0.998. What is the reliability of the engine?
A typical retail transaction consists of severalsmaller steps, which can be considered components subject tofailure. A list of such components might include: Let the eight probabilities of success be .92, .94, .99, .99, .98,.97, .95, and .96. What is the reliability of the system; thatis, the probability that there will be a satisfied customer? Ifyou were the store manager, what do you think should bean acceptable value for this probability? Which componentswould be good candidates for backup, which for redesign?

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