Issue 32, October 2003

When analyzing a system, what is the difference between the reliability block diagram (RBD) and fault tree diagram (FTD) approach?

The most fundamental difference between fault tree diagrams and reliability block diagrams is that you work in the "success space" in an RBD while you work in the "failure space" in an FTD. In other words, the reliability block diagram looks at success combinations while the fault tree diagram looks at failure combinations. In addition, fault trees have traditionally been used to analyze fixed probabilities (i.e. each event that comprises the tree has a fixed probability of occurring) while RBDs may include time-varying distributions for the components success (reliability equation) and other properties, such as repair/restoration distributions. In general, and with some specific exceptions, a fault tree can be easily converted to an RBD. However, it is generally more difficult to convert an RBD into a fault tree, especially if one allows for highly complex configurations. 

For more information on RBDs and FTDs, see ReliaSoft's System Analysis on-line reference, which is an HTML version of the printed theory manual that accompanies BlockSim.

In Weibull++, why doesn't the calculated MLE line track the data points on my probability plot? 

The fitted MLE model does not track the data points because of the differences in the way the plot and the MLE model are generated. The probability plot incorporates estimates of the unreliability in order to provide Y-axis values to go with the failure times on the X-axis. In Weibull++, these unreliability estimates are provided by median ranks or Kaplan-Meier estimates. The maximum likelihood estimator (MLE) method of parameter estimation only uses the failure and suspension (X-axis) data when generating the unreliability model. Consequently, the fitted model may not necessarily track the data points on the plot. However, this does not mean that the model or the plot is "wrong;" it just means that they were generated using two different methods.

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