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:
- Equal Allocation. With this method, the target system reliability is reached by allocating the same reliability to all selected blocks.
- Weighted Allocation. This method is similar to the ARINC apportionment method, designed by the Advisory Group on Reliability of Electronic Equipment, and the Feasibility of Objectives apportionment method, where the improved failure rates are derived based on weighting factors. With this allocation analysis type, the user will have to assign a weight factor to each selected block that is included in the calculation of reliability. If all blocks have the same weight, the allocated reliability will be the same. (For more information on this method, refer to the "Reliability Allocation Using Lambda Predict" article in HotWire Issue 98.)
- Cost Optimized Allocation. With this method, the target system reliability is reached by changing the reliability of each selected component so that the associated cost with improving the reliability is minimized. This is achieved by defining a cost function that associates cost with reliability, and trying to minimize this function while reaching the overall reliability target. (For more information on this method, refer to http://www.ReliaWiki.org/index.php/Reliability_Allocation.)
In this article, we will demonstrate the Cost Optimized Allocation method with a simple 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.
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:
- Early reliability test data at the component level.
- Supplier data.
- Historical information on the same or similar components.
- Engineering judgment if nothing else is available.
Given all that information, we calculate the system reliability at 800 hours to be 86.4767%, as shown in Figure 2.
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).
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:
- Block Name displays the available blocks within the selected diagram. Note that if the block name is a hyperlink, as is the case here, this indicates that the block is a subdiagram.
- Reliability Importance is a metric that describes the relative importance of the block with respect to the reliability of the system. The higher this value is, the higher the effect of improving the reliability of that block to the system reliability.
- Current Reliability is the reliability of each block at the selected end time.
- Maximum Achievable Reliability is the maximum reliability
that each block can theoretically reach (by default, this value is
- Feasibility is an index that represents the difficulty in increasing the block’s reliability. This index can range from Easy to Hard (or from 0.1 to 9.9) and represents any design complexity, technological limitations, supplier issues, etc. that are related to the component. If this is set to Easy, the proposed reliability improvement for the selected block will be higher than if it is set to Hard.
- Target Reliability is a calculated value that shows what the reliability of each block should be in order to reach the system reliability target.
- Equivalent Parallel Units is a calculated value that shows the level of redundancy that would be required in order to reach the system reliability target without making any changes to the reliability of the block.
Given all that information we can run the allocation analysis and obtain the results that are shown in Figure 4.
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.
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.
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.
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.
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.