# Reliability Importance Example

### From ReliaWiki

*This example appears in the article Reliability Importance*.

**Reliability Importance Measures for Failure Modes**

Assume that a system has failure modes , , , , and . Furthermore, assume that failure of the entire system will occur if:

- Mode , or occurs.

- Modes and , and or and occur.

- Mode , or occurs.

In addition, assume the following failure probabilities for each mode.

- Modes and have a mean time to occurrence of 1,000 hours (i.e., exponential with

- Mode has a mean time to occurrence of 100 hours (i.e., exponential with

- Modes , and have a mean time to occurrence of 700,000, 1,000,000 and 2,000,000 hours respectively (i.e., exponential with , and

- Modes and have a mean time to occurrence of 1,000 hours (i.e., exponential with

Examine the mode importance for operating times of 100 and 500 hours.

**Solution**

The RBD for this example is shown next:

The first chart below illustrates . It can be seen that even though , and have a much rarer rate of occurrence, they are much more significant at 100 hours. By 500 hours, , the effects of the lower reliability components become greatly pronounced and thus they become more important, as can be seen in the second chart. Finally, the behavior of can be observed in the Reliability Importance vs. Time plot. Note that not all lines are plainly visible in the plot due to overlap.