# 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 ${{I}_{{{R}_{i}}}}(t=100)\,\!$. 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, ${{I}_{{{R}_{i}}}}(t=500)\,\!$, 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 ${{I}_{{{R}_{i}}}}(t)\,\!$ can be observed in the Reliability Importance vs. Time plot. Note that not all lines are plainly visible in the plot due to overlap.