**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=0.8*3

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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**Question**

**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.