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 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 (QALT) 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.
Example
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-dependent stresses) would then be employed to create the model
for motor B. ReliaSoft's ALTA 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.
Conclusion |