Reliability Importance Example

This example appears in the System analysis reference.

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.