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.