Analytical Diagrams

BlockSim's reliability block diagrams and fault trees can be configured as analytical diagrams (which use exact mathematical solutions for the model but impose limitations on what can be modeled and what results can be obtained) or as simulation diagrams (which provide more modeling options and results but must be analyzed with discrete event simulation).

In the analytical (or algebraic analysis) approach for RBDs and for fault trees using the Equation analysis type, the system's pdf is obtained analytically from each component's failure distribution using probability theory. In other words, this approach involves the determination of a mathematical expression that describes the reliability of the system in terms of the reliabilities of its components. Once the system's reliability function has been determined, other calculations can then be performed to obtain metrics of interest for the system.

Starting in Version 2022, analytical fault trees can also use the Binary Decision Diagram (BDD) analysis type. This is a newer analysis engine that generates a binary decision diagram from the fault tree to calculate results. This newer engine can handle scenarios that the Equation method cannot and generally has better performance than the equation type.

There are several kinds of results available for analytical diagrams:

• The algebraic solution for the diagram (i.e., a mathematical representation of the reliability-wise configuration of the diagram) is available for analytical RBDs and analytical fault trees using the Equation analysis type. It can be viewed in the Equation Viewer.
• The minimal cut sets, or the unique combinations of component failures that can cause system failure, can be viewed in the Cut Sets window.
• The analytical Quick Calculation Pad (QCP) provides quick access to some of the most frequently requested reliability results. These include standard and conditional reliability/probability of failure, failure rate, warranty time, BX information and mean time to failure.
• A wide variety of plots help you to visualize the analytical results. These include plots pertaining to the system and to the blocks, offering information about reliability/unreliability, failure rate, pdf and reliability importance.

In addition, allocation analysis can be performed based on the results from analytical diagrams, except for fault trees using the Binary Decision Diagram analysis type. Allocation analysis helps to decide how the system's reliability can best be improved, based on the reliability importance of the blocks selected for consideration.

Analytical diagrams are appropriate when one is performing "reliability analysis." In the context of BlockSim, we use the term "reliability analysis" to refer to all analyses that do not include repairs or restorations of the component. When considering only the failure characteristics of the components, the analytical approach can be used. However, when both failure and maintenance characteristics need to be considered, the simulation method must be used to take into account the additional events.