OPERATIONS MANAGEMENT(LL)-W/CONNECT
OPERATIONS MANAGEMENT(LL)-W/CONNECT
13th Edition
ISBN: 9781260676310
Author: Stevenson
Publisher: MCG
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Chapter 4.S, Problem 6P

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 spice 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 order to 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)

Expert Solution
Check Mark
Summary Introduction

To determine: The reliability of the robot.

Introduction:

Reliability:

Reliability can be termed as the measure of the capability of a product or any service to perform its intended job under a predetermined set of conditions. The product or service will yield the same results on the repeated trials. It is the degree of consistency of a measure.

Answer to Problem 6P

The reliability of the robot is 0.7876.

Explanation of Solution

Given information:

  • There are 4 components.
  • Reliabilities are 0.98, 0.95, 0.94, 0.90

Calculation of reliability of the robot:

The reliability is calculated by multiplying the probabilities of all the components.

Reliability=0.98×0.95×0.94×0.90=0.7876

Hence, the reliability of the robot is 0.7876.

b)

Expert Solution
Check Mark
Summary Introduction

To determine: The component that should get the backup.

Introduction:

Reliability:

Reliability can be termed as the measure of the capability of a product or any service to perform its intended job under a predetermined set of conditions. The product or service will yield the same results on the repeated trials. It is the degree of consistency of a measure.

Answer to Problem 6P

The component that should get the backup is component 4.

Explanation of Solution

Given information:

  • There are 4 components.
  • Reliabilities are 0.98, 0.95, 0.94, 0.90
  • Each backup will have the same reliability as the component.

Calculation of reliability of the robot:

The reliability is calculated by multiplying the probabilities of all the components.

Reliability=0.98×0.95×0.94×0.90=0.7876

Calculation of reliability of the system:

Component 1 and backup for component 1:

Reliability=0.98+[(10.98)×0.98]=0.98+[0.02×0.98]=0.98+0.0196=0.9996

Reliability of robot=0.9996×0.95×0.94×0.90=0.8034

Component 2 and backup for component 2:

Reliability=0.95+[(10.95)×0.95]=0.95+[0.05×0.95]=0.95+0.0475=0.9975

Reliability of robot=0.98×0.9975×0.94×0.90=0.8270

Component 3 and backup for component 3:

Reliability=0.94+[(10.94)×0.94]=0.94+[0.06×0.94]=0.94+0.564=0.9964

Reliability of robot=0.98×0.95×0.9964×0.90=0.8349

Component 4 and backup for component 4:

Reliability=0.90+[(10.90)×0.90]=0.90+[0.10×0.90]=0.90+0.09=0.99

Reliability of robot=0.98×0.95×0.94×0.99=0.8664

The reliability of component 4 is more when compared with other components.

Hence, the component that should get the backup is component 4.

c)

Expert Solution
Check Mark
Summary Introduction

To determine: The component that should get the backup.

Introduction:

Reliability:

Reliability can be termed as the measure of the capability of a product or any service to perform its intended job under a predetermined set of conditions. The product or service will yield the same results on the repeated trials. It is the degree of consistency of a measure.

Answer to Problem 6P

The component that should get the backup is component 4.

Explanation of Solution

Given information:

  • There are 4 components.
  • Reliabilities are 0.98, 0.95, 0.94, 0.90
  • Backup reliability is 0.92

Calculation of reliability of the robot:

The reliability is calculated by multiplying the probabilities of all the components.

Reliability=0.98×0.95×0.94×0.90=0.7876

Calculation of reliability of the system:

Component 1 and backup for component 1:

Reliability=0.98+[(1-0.98)×0.92]=0.98+[0.02×0.92]=0.98+0.0184=0.9984

Reliability of robot=0.9984×0.95×0.94×0.90=0.8024

Component 2 and backup for component 2:

Reliability=0.95+[(1-0.95)×0.92]=0.95+[0.05×0.92]=0.95+0.0460=0.9960

Reliability of robot=0.98×0.9960×0.94×0.90=0.8258

Component 3 and backup for component 3:

Reliability=0.94+[(1-0.94)×0.92]=0.94+[0.06×0.92]=0.94+0.552=0.9952

Reliability of robot=0.98×0.95×0.9952×0.90=0.8339

Component 4 and backup for component 4:

Reliability=0.90+[(10.90)×0.92]=0.90+[0.10×0.92]=0.90+0.0920=0.9920

Reliability of robot=0.98×0.95×0.94×0.9920=0.8681

The reliability of component 4 is more when compared with other components.

Hence, the component that should get the backup is component 4.

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Chapter 4 Solutions

OPERATIONS MANAGEMENT(LL)-W/CONNECT

Ch. 4.S - Consider the following system: Determine the...Ch. 4.S - A product is composed of four parts. In order for...Ch. 4.S - A system consists of three identical components....Ch. 4.S - A product engineer has developed the following...Ch. 4.S - The guidance system of a ship is controlled by a...Ch. 4.S - One of the industrial robots designed by a leading...Ch. 4.S - A production line has three machines A, B, and C,...Ch. 4.S - Prob. 8PCh. 4.S - A Web server has five major components that must...Ch. 4.S - Repeat Problem 9 under the condition that one of...Ch. 4.S - Hoping to increase the chances of reaching a...Ch. 4.S - An electronic chess game has a useful life that is...Ch. 4.S - A manufacturer of programmable calculators is...Ch. 4.S - Lucky Lumen light bulbs have an expected life that...Ch. 4.S - Prob. 15PCh. 4.S - Prob. 16PCh. 4.S - A major television manufacturer has determined...Ch. 4.S - Prob. 18PCh. 4.S - Determine the availability for each of these...Ch. 4.S - Prob. 20PCh. 4.S - A manager must decide between two machines. The...Ch. 4.S - Prob. 22PCh. 4.S - Auto batteries have an average life of 2.7 years....Ch. 4 - Prob. 1DRQCh. 4 - Prob. 2DRQCh. 4 - Prob. 3DRQCh. 4 - Prob. 4DRQCh. 4 - Prob. 5DRQCh. 4 - Prob. 6DRQCh. 4 - Prob. 7DRQCh. 4 - Prob. 8DRQCh. 4 - a. What is meant by the term life cycle? b. Why...Ch. 4 - Prob. 10DRQCh. 4 - Prob. 11DRQCh. 4 - Prob. 12DRQCh. 4 - Prob. 13DRQCh. 4 - Explain what quality function development is and...Ch. 4 - Prob. 15DRQCh. 4 - Prob. 16DRQCh. 4 - Prob. 17DRQCh. 4 - Prob. 18DRQCh. 4 - Prob. 19DRQCh. 4 - Describe some of the trade-off that are...Ch. 4 - Prob. 2TSCh. 4 - Prob. 3TSCh. 4 - Prob. 1CTECh. 4 - Prob. 2CTECh. 4 - Prob. 3CTECh. 4 - Prob. 4CTECh. 4 - Prob. 5CTECh. 4 - Give two examples of unethical conduct involving...Ch. 4 - Prob. 1PCh. 4 - Prob. 2PCh. 4 - Prepare a service blueprint for each of these...Ch. 4 - Prepare a service blueprint for each of these post...Ch. 4 - Prob. 5PCh. 4 - Prob. 6PCh. 4 - Prob. 7PCh. 4 - Prepare a table similar to that shown in Problem...
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