Sample Answer 
Reliability
Problem 2
Reliability is the probability that a service or product/component will perform according to expectations.
Total Reliability=The product of all reliabilities
To solve the reliability problem of the engine, we sketch a diagram of the components.
Diagram Component
The reliability of the ten parts in the series is given by:
R_s=(R_1 )(R_2 )(R_3 )(R_4 )(R_5 )(R_6 )(R_7 )(R_8 )(R_9 )(R_10 )
Since all the components have equal reliabilities (0.998), the above expression can be reduced to:
R_s=R^10
The average reliability of each component R is 0.998.
Replacing R with 0.998 and solving for will yield the total reliability of the engine.
R_s=〖0.998〗^10
R_s=0.980
Therefore, the reliability of the engine is 0.980.
Problem 10
Reliability is the probability that a service or product/component will perform according to expectations.
System Components
This system has four components, with two of these components containing a backup.
The backup components can be combined to form a single component.
The total reliability of the second component can be calculated as follows:
component reliability=original+backup
The original reliability in the system is marked with an arrow.
0.85+0.85(1-original)
R_2=0.85+0.85(1-0.85)
=0.9775≅0.98
The reliability of the second component is 0.98
The total reliability of the third component can be calculated as follows:
component reliability=original+backup
The original reliability in the system is marked with an arrow.
=0.90+0.90(1-original)
R_2=0.90+0.90(1-0.90)
=0.99
The reliability of the second component is 0.99
After eliminating the backup systems, the final system can be represented as follows:
Final System
The total reliability of this system can be calculated by multiplying the reliabilities of the components making up the system, including backups.
Total Reliability=The product of all reliabilities
R_s=(R_1 )(R_2 )(R_3 )(R_4 )
R_s=0.9×0.9775×0.99×0.95
R_s=0.83
Therefore, the reliability of the system is 0.83
References
Reid, R. D., & Sanders, N. R. (2016). Operations Management, Binder Ready Version: An Integrated Approach. John Wiley & Sons.
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Question 
Total Quality Management: Reliability
Complete the following problems in your textbook:
Reliability
- Problem 2 on page 179.
- Problem 10 on page 180.
For help on how to complete these problems, see the Solved Problems on pages 178–179.
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