Two types of analytical calculations can be performed using RBDs (and BlockSim): static reliability calculations and time-dependent reliability calculations. Systems can contain static blocks, time-dependent blocks or a mixture of the two. Analytical computations are discussed in the RBDs and Analytical System Reliability and Time-Dependent System Reliability (Analytical) sections of this on-line reference.
Static analytical calculations are performed on RBDs that contain static blocks. A static block can be interpreted either as a block with a reliability value that is known only at a given time (but the block's entire distribution is unknown) or as a block with a probability of success that is constant with time. Static calculations can only be performed in the analytical mode and not the simulation mode. Figure 2.10 illustrates a static RBD.
Figure 2.10: Reliability block diagram (RBD) of a static system.
Time-dependent analysis looks at reliability as a function of time. That is, a known failure distribution is assigned to each component. The time scale in BlockSim can assume any quantifiable time measure, such as years, months, hours, minutes or seconds, and also units that are not directly related to time, such as cycles or miles of use. In many of the discussions and examples that follow, and to maintain generality, time units may be omitted or a general time unit (tu) may be used. It is very important to remember that even though any time unit may be used, the time units used throughout an analysis must be consistent in order to avoid incorrect results.
The primary objective in system reliability analysis is to obtain a failure distribution of the entire system based on the failure distributions of its components, as illustrated in Figure 2.11.
Figure 2.11: Obtaining the system' s pdf from the pdfs of the components.
When considering only the failure characteristics of the components, the analytical approach should be used. However, when both the failure and maintenance characteristics need to be considered, the simulation method must be used to take into account the additional events.
In the analytical (or algebraic analysis) approach, the system's pdf is obtained analytically from each component's failure distribution using probability theory. In other words, the analytical approach involves the determination of a mathematical expression that describes the reliability of the system in terms of the reliabilities of its components (remember also that cdf(t) = 1 - R(t)).
The advantages of the analytical approach are:
The mathematical expression for the system's cdf is obtained.
Conditional reliability, warranty time and other calculations can be performed.
Analyses involving components with static reliability values can be performed.
Ancillary analyses can be performed, such as optimized reliability allocation, reliability importance computation of components, etc.
The disadvantage of the analytical approach is:
Analyses that involve repairable systems with multiple additional events and/or other maintainability information are very difficult (if not impossible) to solve analytically. In these cases, analysis through simulation becomes necessary.
If one includes information on the repair and maintenance characteristics of the components and resources available in the system, other information can also be analyzed/obtained, such as system availability, throughput, spare parts utilization, life costs etc. This can be accomplished through discrete event simulation.
In simulation, random failure times from each component's failure distribution are generated. These failure times are then combined in accordance with the way the components are reliability-wise arranged within the system. The overall results are analyzed in order to determine the behavior of the entire system.
The advantages of the simulation approach are:
It can be used for highly complex scenarios involving a multitude of probabilistic events, such as corrective maintenance, preventive maintenance, inspections, imperfect repairs, crew response times, spare part availability, etc. When events such as these are considered, analytical solutions become impossible when dealing with real systems of sufficient complexity.
The discrete event simulation also has the capability of:
Examining resource utilization, efficiency and costs.
Optimizing procedures and resource allocation.
Analyzing relationships between systems and components.
Maximizing throughput.
Minimizing work downtimes.
The disadvantages of the simulation approach are:
It can be time-consuming.
The results are dependent on the number of simulations.
There is a lack of repeatability in the results due to the random nature of data generation.
Simulation is discussed in the Repairable Systems Analysis Through Simulation and Additional Analyses sections of this on-line reference.
See Also:
Overview of System Reliability
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