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Using Reliability Allocation Analysis to Set Component Specifications

One of the most common challenges in reliability engineering is translating reliability requirements at the system level to requirements at the component level. This effort is challenging because it involves allocating reliability to components so that the system performance goal is met while at the same time considering development costs, design complexities, supplier issues, etc. This article describes the allocation analysis methods available in BlockSim 8 and provides an example of how, given a system reliability goal, one can flow reliability requirements all the way down to the component level.

Allocation Analysis Types in BlockSim

BlockSim 8 offers three types of allocation analysis:

In this article, we will demonstrate the Cost Optimized Allocation method with a simple example.

Example

Consider a system that is comprised of two major subsystems (Subsystem A and Subsystem B). Each subsystem includes some assemblies and each assembly is composed of a few components. Figure 1 shows the reliability block diagram of the system, starting from the subsystem level and going all the way down to the component level.

System reliability block diagram
Figure 1 - System reliability block diagram

For this example, the target reliability that we have set for the system is 95% at 800 usage hours (which corresponds to one year of operation).

Table 1 shows the failure distribution parameters for each of the components in the system.

Table 1 - Failure distribution parameters for each component in the system

Component Failure Distribution Parameter 1 Parameter 2
Comp. 0 Weibull Beta = 2 Eta = 5,000
Comp. 1 Weibull Beta = 1.5 Eta = 4,500
Comp. 3 Weibull Beta = 1.5 Eta = 8,965
Comp. 4 Weibull Beta = 1 Eta = 8,000
Comp. 5 Lognormal Log-Mean = 10 Log-Std. = 1.4
Comp. 6 Weibull Beta = 3 Eta = 10,000
Comp. 7 Normal Mean = 10,000 Std. = 200
Comp. 8 Normal Mean = 8,000 Std. = 100
Comp. 9 Weibull Beta = 1.5 Eta = 7,000

We obtained the failure information for each component from a combination of:

Given all that information, we calculate the system reliability at 800 hours to be 86.4767%, as shown in Figure 2.

System reliability at 800 hours
Figure 2 - System reliability at 800 hours

Obviously this is well below our 95% target so our next question is what components should we improve and by how much in order to reach that target. Furthermore, we want to achieve this target by keeping our development costs to a minimum. This is where the allocation analysis tool can be very useful. Figure 3 shows the Allocation Analysis window at the system level (where the system is composed of two subsystems).

Allocation analysis inputs at the system level
Figure 3 - Allocation analysis inputs at the system level

As it can be seen in the control panel, we have chosen the Cost Optimized allocation type in order to minimize cost. We also entered the specified system target reliability of 95% at 800 hours in the Inputs area.

For the Cost Optimized method, the columns displayed in the Allocation Analysis window are:

Given all that information we can run the allocation analysis and obtain the results that are shown in Figure 4.

Allocation analysis results at the system level
Figure 4 - Allocation analysis results at the system level

As one would expect, because we set the feasibility of Subsystem A to Easy (as it is a new design that can be improved) and we set the feasibility of Subsystem B to Hard (as it is a more mature design where making changes would be difficult), the results indicate that Subsystem B’s reliability should remain unchanged, while Subsystem A’s reliability should be increased to approximately 98.8% in order to reach our target system reliability.

The next step is to determine how the components within Subsystem A should be improved in order to reach that new reliability target. We can do this by clicking the Subsystem A hyperlink in the Block Name column. This creates a new tab for Subsystem A at the bottom of the Allocation Analysis window. Figure 5 shows the new subsystem tab. Note that the target reliability in the Inputs area of the control panel is automatically set to the value calculated for Subsystem A in the previous step.

Allocation analysis inputs for Subsystem A
Figure 5 - Allocation analysis inputs for Subsystem A

Now we can follow the same steps in order to allocate reliability to each of the assemblies with Subsystem A. As it can be seen in Figure 5, the reliability importance of Assembly A is significantly higher than that of Assembly B. So we would really want to focus only on that because it would provide the highest return on our efforts. We do this by clearing the check boxes next to each Assembly B block.

After running the analysis, we find that the new reliability target for Assembly A is approximately 99.35%, as shown in Figure 6.

Allocation analysis results for Subsystem A
Figure 6 - Allocation analysis results for Subsystem A

Finally, we can take the allocation analysis all the way to the component level by allocating reliability to the two components within Assembly A. In this case, we set the feasibility factors as follows: Component 0 is set to 6 and Component 1 is set to 4. Figure 7 shows the results.

Allocation analysis results for Assembly A
Figure 7 - Allocation analysis results for Assembly A

Therefore, if we improve Component 0 to 99.77% reliability and Component 1 to 99.58%, we will have reached the overall system target of 95% while at the same time minimizing the associated cost of reaching that target.

Conclusion

Using this simple example, we illustrated how you can use the Cost Optimized allocation analysis in BlockSim 8 in order to translate a given system reliability specification into reliability requirements at the component level, while minimizing the associated costs in doing so. For the other two analysis types, you would use the same Allocation Analysis tool but select a different option from the Allocation Type drop-down list. The columns in the table will be updated to reflect the analysis type that is currently selected.

 
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