Reliability Importance Example

This example appears in the article Reliability Importance.

Reliability Importance Measures for Failure Modes

Assume that a system has failure modes $$A$$,  $$B$$ ,  $$C$$ ,  $$D$$ ,  $$E$$  and  $$F$$. Furthermore, assume that failure of the entire system will occur if:


 * •	Mode $$B$$,  $$C$$  or  $$F$$  occurs.
 * •	Modes $$A$$  and  $$E$$,  $$A$$  and  $$D$$  or  $$E$$  and  $$D$$  occur.

In addition, assume the following failure probabilities for each mode.
 * •	Modes $$A$$  and  $$D$$  have a mean time to occurrence of 1,000 hours (i.e., exponential with  $$MTTF=1,000).$$
 * •	Mode $$E$$  has a mean time to occurrence of 100 hours (i.e., exponential with  $$MTTF=100).$$
 * •	Modes $$B$$,  $$C$$  and  $$F$$  have a mean time to occurrence of 700,000, 1,000,000 and 2,000,000 hours respectively (i.e., exponential with  $$MTT{{F}_{B}}=700,000$$,  $$MTT{{F}_{C}}=1,000,000$$  and  $$MTT{{F}_{F}}=2,000,000).$$

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 $${{I}_}(t=100)$$. It can be seen that even though $$B$$,  $$C$$  and  $$F$$  have a much rarer rate of occurrence, they are much more significant at 100 hours. By 500 hours, $${{I}_}(t=500)$$, 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 $${{I}_}(t)$$  can be observed in the Reliability Importance vs. Time plot. Note that not all lines are plainly visible in the plot due to overlap.