# Modeling Specific Functions of a Ring Network Topology in BlockSim

This is the second part of a two-part article that addresses how to create a reliability block diagram (RBD) model of a ring network with bi-directional communication paths using BlockSim that will provide information on both the system availability and the availability of particular communication paths. In the October 2016 issue of Reliability HotWire, we discussed how to create the system-level RBD model starting from the ring network schematic. In this article, we demonstrate how to augment the model to incorporate blocks that represent the state of communication between the HMI and the connected devices.

When simulating an RBD in BlockSim, the system- and block-level results are computed. Using the Simplified Ring Network RBD as presented in Part 1, we could answer the following questions about availability:

• What percent of the time is the system up and running (i.e., what is the system availability)?
• What percent of the time is each block up and running (i.e., what is the availability of each block)?

Suppose that in addition to the above questions, we also want to answer questions about the availability of functions different from the function necessary for system success, such as:

• What percent of the time will the PLC communicate with at least one HMI (i.e., what is the availability of the group of items necessary for the PLC to communicate with HMI 1 and/or HMI 2)?
• What percent of the time will I/O Board 2 communicate with HMI 1 (i.e., what is the availability of the group of items necessary for I/O Board 2 to communicate with HMI 1)?
• What percent of the time will HMI 2 communicate with both I/O Board 1 and I/O Board 2 (i.e., what is the availability of the group of items necessary for I/O Board 1 and I/O Board 2 to communicate with HMI 2)?

There is no way to determine these availabilities from the RBD presented in Part 1. We present a method of incorporating this information into the simulation results below.

In order to illustrate the method, consider the case where the analyst wants to answer the following question:

• What is the availability of the communication path between the PLC and HMI 1?

The first step is to build a subdiagram that represents the logic for the successful communication between the PLC and at least one HMI, as shown in Figure 1. Note that each block on the subdiagram is assigned to a mirror group since these blocks represent the same components as the blocks in the system level diagram.

Figure 1 - Subdiagram representing PLC communicating with HMI

The second step is to modify the system-level RBD to include the subdiagram representing successful communication between the PLC and at least one HMI in such a way that the system-level calculations are not affected. Figure 2 shows the construct that we use to accomplish this, which effectively short circuits the subdiagram so that it cannot bring the system down. (Note that this figure also includes the final node in the original system level RBD.)

Figure 2 - Addition of subdiagram block that does not impact system reliability

Figure 3 shows the updated system-level diagram.

Figure 3 - Simplified Ring Network RBD with subdiagram block that does not impact system reliability

The third step is to change the default BlockSim analysis settings to include the subdiagram availability in the block results by selecting the Report subdiagram results check box on the Analysis Settings page of the control panel. The results for the "PLC Communicates with HMI" subdiagram will be included in both the Block Summary and Block Details sections of the simulation results.

Table 1 shows the component failure and repair properties that we assigned to the blocks in the RBD.

 Component Name Failure Properties Repair Properties Distribution MTTF (h) Distribution Beta Eta (h) Ethernet Cable Exponential 40000 Weibull 3.0 12 Ethernet Switch Exponential 75000 Weibull 2.5 24 PLC Exponential 60000 Weibull 2.0 48 I/O Board Exponential 50000 Weibull 2.0 48 HMI Exponential 15000 Weibull 2.0 72

We then ran a simulation with an end time of 20 years. Table 2 shows a condensed version of the Block Summary, which contains both the results for each individual block and the subdiagram representing the communication between the PLC and at least one HMI.

 Block Name RS FCI (%) RS DTCI (%) Mean Av. (All Events) (%) Expected # of Failures System Downing Events Block Downtime (h) PLC 0.00 0.00 99.9333 2.775 0 116.80 I_O_Board_1 0.00 0.00 99.9135 3.545 0 151.52 I_O_Board_2 0.00 0.00 99.9138 3.545 0 150.98 HMI 1 48.18 59.15 99.5731 11.777 0.053 748.00 HMI 2 33.64 35.90 99.5725 11.702 0.037 748.93 ENS 1 1.82 0.94 99.9714 2.375 0.002 50.02 ENS 2 2.73 1.05 99.9727 2.303 0.003 47.80 ENS 3 1.82 0.29 99.9713 2.317 0.002 50.33 ENS 4 0 0 99.9715 2.354 0 49.97 ENS 5 1.82 0.27 99.9709 2.386 0.002 50.99 C 12 0 0 99.9723 4.524 0 48.45 C 15 6.36 1.44 99.9732 4.398 0.007 46.90 C 23 3.64 0.95 99.9735 4.336 0.004 46.46 C 30 0 0 99.9730 4.369 0 47.32 C 34 0 0 99.9732 4.424 0 46.95 C 40 0 0 99.9729 4.440 0 47.49 C 45 0 0 99.9734 4.354 0 46.59 C 50 0 0 99.9734 4.323 0 46.63 C 101 0 0 99.9728 4.479 0 47.72 C 102 0 0 99.9727 4.425 0 47.82 C 201 0 0 99.9730 4.411 0 47.23 C 202 0 0 99.9737 4.276 0 46.03 PLC Communicates with HMI 100.00 100.00 99.8760 9.677 0.110 217.22

## Conclusion

This article presented a procedure for incorporating subsystem availability results into a system-level diagram. We first constructed a subdiagram that represents the subsystem success. Then we incorporated the subdiagram into the system-level RBD. Finally, we set up the analysis to include subsystem-level results in the Block Summary and Block Details sections of the simulation results. This method can be applied to any scenario in which the availability must be determined for a group of components that perform a function separate from the function necessary for the system success modeled in the system level RBD.