Quarter 2, 2003:  Volume 3, Issue 3

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Using QALT Models to Analyze System Configurations with Load Sharing

When components of a system operate in a load sharing configuration, each component supports a portion of the total load for that aspect of the system. When one or more load sharing components fail, the operating components must take on an increased portion of the load in order to compensate for the failure(s). Therefore, the reliability of each component is dependent upon the performance of the other components in the load sharing configuration. This article demonstrates the use of QALT life-stress relationship models to analyze the effect of this dependency in systems with load sharing configurations. One of the many breakthroughs of ReliaSoft's BlockSim 6 software is its ability to handle such dependency among blocks within a reliability block diagram (RBD) in both the exact analytical mode and the simulation mode. 

Applying QALT Models to Load Sharing Configurations
In general, when one creates a reliability block diagram, redundant blocks are assumed to be independent of each other. In other words, the failure of one block does not alter the failure characteristics of the remaining blocks in the redundant configuration. However, in a load sharing configuration where dependency among the redundant blocks is assumed, the failure of one block does alter the failure characteristics of the remaining blocks. In such configurations, the failure of one component causes the other component(s) to work harder, thus changing the failure characteristics of the operating component(s). In most cases, this has the effect of accelerating the failure mechanism(s) for the remaining component(s). 

Traditionally in a reliability block diagram, one assumes independence and thus an item's failure characteristics can be fully described by its failure distribution. However, if the configuration includes load sharing redundancy, then a single failure distribution is no longer sufficient to describe an item's failure characteristics. Instead, the item will fail differently when operating under different loads and the load applied to the component will vary depending on the performance of the other component(s) in the configuration. Therefore, a more complex model is needed to fully describe the failure characteristics of such blocks. This model must describe both the effect of the load (or stress) on the life of the product and the probability of failure of the item at the specified load. The models, theory and methodology utilized in Quantitative Accelerated Life Testing_SM (QALT_SM) data analysis can be utilized to obtain the desired model for this situation. The objective of QALT analysis is to relate the applied stress to life (or a life distribution). Identically in the load sharing case, one again wants to relate the applied stress (or load) to life. Figure 1 graphically illustrates the probability density function (pdf) for a standard item, where only a single distribution is required. Figure 2 represents a load sharing item by utilizing a 3-D surface that illustrates the pdf, load and time. Figure 3 shows the reliability curve for a load sharing item vs. the applied load. 

Figure 1: Standard item with pdf

Figure 2: Load sharing item with pdf and life-stress

Figure 3: 3-D graph of reliability vs. the applied load

Example 
Having defined the applicable models for load sharing units, the next task is to obtain such models from data. Obviously, tests performed under different load conditions for each unit can be utilized, much like traditional QALT analysis. An alternative approach (and in some ways a better approach) is to look at data from the combined operations of the load-sharing units. As an example, consider a system that contains two motors in a redundant configuration (i.e. only one of the two motors is required for system operation). If both motors are functioning, the load is shared between the motors. If one of the motors fails, the entire load is then shifted to the surviving motor. If both motors fail, the system is then considered to have failed. Furthermore, assume that when both units are operating, the load is equally shared (i.e. 50% on each motor). This type of relationship is represented in ReliaSoft’s BlockSim 6 software with a Load Sharing Container, as shown below. 

Table 1 presents the data (times-to-failure) for the failure of the system and the motor. The data set was obtained from a life test on 18 such systems operating continuously. The Time to First Event column contains the times at which one of the two motors failed. The Event Description column identifies which one of the two motors failed at each time and the Time to System Failure column contains the time-to-failure of the surviving motor. 

Table 1: Data set for two motors in a load sharing configuration

If load sharing were not present, then building a life model for each motor would be trivial. One would simply fit a life model to each motor individually, based on the times-to-failure for each motor, and analyze each motor individually. However, since load sharing is present, this analysis would be incorrect. To address the load sharing, a more complex data set needs to be utilized. 

To illustrate the analysis approach, consider motor B. In System 1, the time-to-failure of motor B is 65 hours at a 50% loading. However in System 2, the time-to-failure of motor B is 148 hours with the first 84 hours of operation at 50% loading and the next 64 hours (from 84 to 148 hours) at 100% loading. A better way to illustrate the time-to-failure of motor B in System 2 is to think of a unit subjected to a step-stress profile, as shown in Figure 4. This would then be repeated for all systems and for all motor B failures. A cumulative damage model (using time-varying stresses) would then be employed to create the model for motor B. ReliaSoft's ALTA 6 PRO software can be utilized for such analysis. This procedure can then be repeated for motor A. When the analysis is complete, the models and their parameters can then be incorporated inside the block diagram for system analysis with the assumption of item dependency (or load sharing). ReliaSoft’s BlockSim 6 software supports such analysis and provides integration with ALTA to define the load-dependent failure characteristics of load sharing components. 

Figure 4: Load vs. Time plot (step-stress profile)

Conclusion 
This article discussed the analysis of components in a system configuration with load sharing redundancy, where the failure characteristics of each component are dependent upon the performance of the other components in the configuration. To accomplish this, we used the tools and models from QALT analysis principles and also required a sophisticated RBD tool that is capable of incorporating these QALT models and dependencies. In closing, it should also be pointed out that even though RBDs are traditionally thought of as tools to analyze a system made up of components, RBDs can also be used to analyze a single component from a failure mode perspective. Each block in the RBD can be a failure mode and dependent failure modes can be also included using the analysis concepts for load sharing blocks.