Reliability

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 details.

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 it 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.

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Problem 10

Reliability is the probability that a service or product/component will perform according to expectations.

This system has four components, with two of these components containing a backup.

The backup components can be combined to form a single part.

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 design can be represented as follows:

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

Other Related Post: Capital Market In a “perfect world.”

References

Reid, R. D., & Sanders, N. R. (2016). Operations Management, Binder Ready Version: An Integrated Approach. John Wiley & Sons.

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Total Quality Management: Reliability

Complete the following problems in your textbook:

• Problem 2 on page 179.
• Problem 10 on page 180.

For help completing these problems, see the Solved Problems on pages 178–179.

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