Question

In: Operations Management

A smoke detector consists of three components with reliabilities of 0.995, 0.994, and 0.996.

A smoke detector consists of three components with reliabilities of 0.995, 0.994, and 0.996.

a.         What is the reliability of the system?

b.         If identical backups are provided for each component, what is the reliability of the new system? Assume switch reliabilities of 1.0.

c.         What is the reliability of the system in part b if the switch reliabilities are 0.998?

Solutions

Expert Solution

(a)

The system reliability in this case is very high.

= 0.995 * 0.994 * 0.996=0.98507388 or 98.51%. It means that, in the development cycle, the firm may depend on its program. Recall that in such a case the system's reliability will affect the other's reliability.

In any case, there is a fault in the first system, and then it may affect the entire process. This is why some firms will always have a back-up to make sure the components are not exposed to a lot of failures.

(b)

First component reliability + (second component * (1-fist system reliability) * reliability of third component.

We will therefore have: 0.995 + (0.994 * (1-0.995) * 0.996= (0.995 + 0.00497) * 0.996= 0.9959012 or 99.597012%. This is an indication that due to the introduction of the backups, system reliability has improved.

(c)

This is measured precisely as follows: 0.9959012 * 0.998= 0.99397817976 or 99.398%. The system's reliability has changed because the system switch is not 100 % reliable. The reliability of the systems is thus normally dependent on the reliability of the other components in the same line.

 

keosha answered 1 year ago
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