Reliability Importance Example

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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.


Plot of


Plot of


Plot of
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