Production and Operations Analysis, Seventh Edition
7th Edition
ISBN: 9781478623069
Author: Steven Nahmias, Tava Lennon Olsen
Publisher: Waveland Press, Inc.
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Chapter 13.4, Problem 17P
a
Summary Introduction
Interpretation:
Reliability of single component system.
Concept Introduction:
Exponential distribution is a probabilitydistribution which finds probability of an event to occur between independent constant rate and continous rate.
b
Summary Introduction
Interpretation:
Reliability of two component system in series.
Concept Introduction:
Exponential distribution is a probabilitydistribution which finds probability of an event to occur between independent constant rate and continous rate.
c
Summary Introduction
Interpretation:
Reliability of two component system in parallel.
Concept Introduction:
Exponential distribution is a probabilitydistribution which finds probability of an event to occur between independent constant rate and continous rate.
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An operation consists of two steps , the first of which has a reliability of 97% and the second a reliability of 99%. What is the probability that the operation will fail?
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Assume that the system still costs $600 to fix every time it breaks down, and you are going to run the system 1000 times. You are considering improving your system. You have contacted a backup supplier of component 1. She tells you that the backup for component 1 will cost $50,000. What would the minimum reliability of the backup need to be to make the purchase worthwhile? (keep 4 decimals for intermediate calculations)
If the backup computer must be activated by a switch in the event that the first computer fails, and the switch has a reliability of .98, what is the overall reliability of the system? (Both the switch and the backup computer must function in order for the backup to take over.)
Chapter 13 Solutions
Production and Operations Analysis, Seventh Edition
Ch. 13.1 - Prob. 3PCh. 13.1 - Prob. 4PCh. 13.1 - Prob. 5PCh. 13.1 - Prob. 6PCh. 13.2 - Prob. 7PCh. 13.2 - Prob. 9PCh. 13.3 - Prob. 13PCh. 13.3 - Prob. 14PCh. 13.4 - Prob. 15PCh. 13.4 - Prob. 16P
Ch. 13.4 - Prob. 17PCh. 13.4 - Prob. 18PCh. 13.4 - Prob. 19PCh. 13.4 - Prob. 20PCh. 13.6 - Prob. 21PCh. 13.6 - Prob. 22PCh. 13.6 - Prob. 23PCh. 13.6 - Prob. 24PCh. 13.6 - Prob. 25PCh. 13.7 - Prob. 26PCh. 13.7 - Prob. 27PCh. 13.7 - Prob. 28PCh. 13.7 - Prob. 30PCh. 13.7 - Prob. 31PCh. 13.7 - Prob. 32PCh. 13.7 - Prob. 33PCh. 13.7 - Prob. 34PCh. 13.8 - Prob. 35PCh. 13.8 - Prob. 36PCh. 13.8 - Prob. 37PCh. 13.8 - Prob. 38PCh. 13.8 - Prob. 39PCh. 13.8 - Prob. 40PCh. 13.8 - Prob. 41PCh. 13 - Prob. 42APCh. 13 - Prob. 43APCh. 13 - Prob. 44APCh. 13 - Prob. 45APCh. 13 - Prob. 46APCh. 13 - Prob. 48APCh. 13 - Prob. 49APCh. 13 - Prob. 51APCh. 13 - Prob. 52APCh. 13 - Prob. 53AP
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- A component has a reliability that fits the exponential distribution. The Mean Time Between Failure for the component is 2500 cycles. What is the probability that the component will not fail before 7500 cycles? ( don't hand writing solution)arrow_forwardBanks have card readers on the outside doors to individuals branches for access to the ATM lobby for off banking hours. In this example, a bank has decided to use two card readers hooked up in parallelredundancy where the customer can use either card reader to gain entry to the lobby. Assume that the percentage of failure for the card reader is 5%, find the overall system reliability, Rs .arrow_forwardCAN 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?arrow_forward
- 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.arrow_forwardAn early warning security fence has three major components each must perform in order for the system to perform. Their reliabilities are .4, .3, and .2. The system reliability is equal to:arrow_forwardDue to the extreme cost of interrupting production, a firm has two standby machines available in case a particular machine breaks down. The machine in use has a reliability of .94, and the backups have reliabilities of .90 and .80. In the event of a failure, either backup can be pressed into service. If one fails, the other backup can be used. Compute the system reliability.arrow_forward
- 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?arrow_forwardAn office security system at PAC Ltd has two component parts, both of which must work for the system to function. Part 1 has a reliability of 80 percent, and part 2 has a reliability of 98 percent. Compute the reliability of the system.arrow_forwardReliability metrics includes: Select one: a. Probability of failure on demand, Rate of occurrence of failures/Mean time to failure, and Availability b. Probability of failure on demand c. Availability d. Rate of occurrence of failures/Mean time to failurearrow_forward
- Consider a product with three components in series, with reliabilities of 0.90, 0.80, and 0.99 for components A, B, and C, respectively. Furthermore, component B uses a backup that also has a reliability of 0.80. What is the reliability of the system?arrow_forwardRick Wing, salesperson for Wave Soldering Systems, Inc. (WSSI), has provided you with a proposal for improving the temperature control on your present machine. The machine uses a hot-air knife to cleanly remove excess solder from printed circuit boards; this is a great concept, but the hot-air temperature control lacks reliability. According to Wing, engineers at WSSI have improved the reliability of the critical temperature controls. The new system still has the four sensitive integrated circuits controlling the temperature, but the new machine has a backup for each. The four integrated circuits have reliabilities of 0.84 0.86 0.88 and 0.90 The four backup circuits all have a reliability of 0.84 Part 2 a) The overall reliability of the new temperature controller = enter your response here% (enter your response as a percentage rounded to two decimal places).arrow_forwardRick Wing, salesperson for Wave Soldering Systems, Inc. (WSSI), has provided you with a proposal for improving the temperature control on your present machine. The machine uses a hot-air knife to cleanly remove excess solder from printed circuit boards; this is a great concept, but the hot-air temperature control lacks reliability. According to Wing, engineers at WSSI have improved the reliability of the critical temperature controls. The new system still has the four sensitive integrated circuits controlling the temperature, but the new machine has a backup for each. The four integrated circuits have reliabilities of 0.840.84, 0.860.86, 0.880.88, and 0.900.90. The four backup circuits all have a reliability of 0.840.84. Part 2 a) The overall reliability of the new temperature controller = 92.2592.25% (enter your response as a percentage rounded to two decimal places). Part 3 b) If you pay a premium, Wing says he can improve all four of the backup units to 0.870.87.…arrow_forward
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