Estimating Failures for a Fleet of Vehicles with Different Configurations
When purchasing a product, it is very common for a customer to have options with regards to what features they get. This is perhaps most evident when purchasing a vehicle. Does the customer buy the base model with very few features, or do they buy a higher-end model that can come with a bigger engine, a turbo, the premium sound system, a sunroof, etc.? As a manufacturer of these vehicles, we are likely interested in not only the reliability/availability of a particular model, but also the overall number of expected failures our maintenance department might see over the warranty period across all vehicles sold in a given time period. In this article, we will discuss a methodology that can be utilized to estimate the average number of failures per vehicle model and also the total number of failures our maintenance team is expected to see.
As this type of problem involves complex systems and estimating the expected number of failures for each system, we will be using simulation via reliability block diagrams (RBDs) in BlockSim and a flowchart in RENO. We will use the BlockSim RBDs to build the individual vehicle models so that we can run simulations on each vehicle. We will also use a RENO flowchart to keep track of our results and provide certain inputs into our overall fleet simulation. These inputs can vary greatly depending on what type of information we have available or what we are trying to solve for.
In this particular example, we will assume that there are three different vehicle models to choose from: base model, mid-level and high-end. We will further assume that we are interested in an analysis across 1000 vehicles sold, where the customer will choose the base model 60 percent of the time, the mid-level model 25 percent of the time, and the high-end model 15 percent of the time. The warranty period of interest is for the first 36000 miles for each vehicle.
In order perform our fleet level analysis, the first step is to create system level representations for our three different vehicle models to use during the simulations. Therefore, we build an RBD for each vehicle model. So as to not overcomplicate this example, we limit our vehicle models to four subsystems each, with each subsystem having between three to five components, depending on the model type.
Table 1 shows the subsystems and components in each vehicle model.
Table 1: Vehicle systems
Figure 1 shows the reliability model for each of the components.
Figure 1: Reliability models
Because we assume that the vehicle is not operational while under repair, we set the repair duration for each component to zero.
Figures 2 to 6 show the RBDs for the base model vehicle. The other model RBDs are similar to the base model except for the addition of the extra components in series within the subsystems.
Figure 2: Base model system level RBD
Figure 3: Base body subsystem
Figure 4: Base electronics subsystem
Figure 5: Base engine subsystem
Figure 6: Base transmission subsystem
After we have created the RBDs for all three vehicle models, we need to create a RENO flowchart that will use the RBDs. The RENO flowchart needs to take into account the number of vehicles sold, the ratio of the various models purchased by the customers, as well as the warranty period of interest. It also needs to keep track of the results that we are interested in.
Figure 7 shows the four variables that we will use to keep track of our inputs into the RENO flowchart.
Figure 7: Variables used in RENO Flowchart
Figure 8 shows the RENO Simulation Definitions that we will use to link our RENO flowchart to our BlockSim RBDs so that the proper RBD is simulated for each vehicle within our fleet.
Figure 8: RENO Simulation Definitions
In our RENO flowchart, we will keep track of how many failures each vehicle saw throughout our simulation, the average number of failures per vehicle model and the total number of failures across the entire fleet (i.e., the expected number of service calls the maintenance department would see). Figure 9 shows the completed RENO flowchart.
Figure 9: RENO flowchart
In this flowchart, we use a Do Loop to perform our analysis on the given number of vehicles (using the vehicles_sold variable), and we use a randomly generated value and a branch gate to select which particular vehicle model we run the current loop with (using the fraction_base_model and fraction_mid_model variables). Using variables rather than hardcoded values makes our RENO flowchart robust so that we can easily change the parameters of our desired simulation.
For the individual vehicle paths, we use an array based result storage block to keep track of the number of failures for the individual vehicle, and an averaging result storage block to get the average for all of the vehicles of that model type. For the overall number of failures, we use a normalized sum result storage block.
When we are ready to perform our simulation, we have to remove the seed from our RENO simulation to ensure that we do not get the exact same number of failures for each vehicle that we run in our RBDs (as the BlockSim RBDs use the seeding setting from the RENO flowchart).
Figure 10 shows the simulated RENO results. In this particular simulation, the average number of failures over 36000 miles for our fleet was 2.76 for the base model, 3.90 for the mid-level model, and 4.59 for the high-end model. These results were as expected, as the mid-level and high-end models have more components that can possibly fail during operation of the vehicle. Also, the total expected number of failures for our fleet of 1000 vehicles was 3356.
Figure 10: Simulated RENO flowchart
Figure 11 shows the log of the individual failures for the base model results that we can use to do statistical analyses on the base model alone, such as number of failures for the bottom or top 10th percentile vehicle. We can also perform the same type of analyses on the other model types as well.
Figure 11: Log of Individual Base Model Failure Counts
While it is possible to analyze and simulate individual systems using BlockSim's RBDs, when combined with RENO flowcharts, we can take the simulation analysis to another level of complexity and analyze entire fleets with multiple types of systems and get various metrics of interest for the entire fleet. This methodology could be extended to allow one to predict more complicated scenarios, such as the number of failures on fleets of vehicles already out in the field where the various vehicles have different miles currently on them.