# Estimating Mean Time Between Maintenance (MTBM) Using BlockSim

Maintenance includes all activities necessary to maintain the system in good condition. The Mean Time Between Maintenance (MTBM) estimate is necessary for designing a planned general scheme for maintenance and support of systems/subsystems in the operational environment. In this article, we perform a simple example using BlockSim 8 to show how a maintenance action that brings a block/component down can affect the entire system.

## Mean Time Between Maintenance (MTBM)

MTBM is a measure of the reliability taking into account the maintenance policy, which is the total number of life units expended by a given time, divided by the total number of maintenance events (scheduled and unscheduled) performed on that item.

During the operating cycle of the system, we need to know an average time when a maintenance action will be required to fix the failed component/LRU (Lowest Replaceable Unit). It must be kept in mind that even though the system may not be down due to a failed component/LRU, corrective maintenance will be required to repair/replace the failed item.

It is often true that whenever there is a failure of an LRU, it will bring the system down and initiate a maintenance action. Once the LRU has been replaced, the system begins to function normally until the next failure. The MTBM is calculated by dividing the system uptime by the total number of maintenance events. This can be better understood using the following example.

## Example

Consider the case of a system having four components A, B, C and D, where components B and C are in a parallel configuration.

The failure and repair distributions of the components are shown in the following table.

 Component Failure Distribution P1 P2 Repair Distribution P1 P2 A Weibull 3 1,300 Normal 50 10 B Weibull 1.6 900 Normal 30 2 C Weibull 1.4 1,200 Normal 30 2 D Weibull 3 1,500 Normal 40 3

Figure 1 shows how the components in the system are reliability-wise connected.

Figure 1: Parallel configuration

You can see that because blocks B and C are parallel to each other, only one of them is needed for the successful completion of the mission.

However, if any maintenance activity will bring the system down, then, in terms of maintainability, this parallel configuration is the same as the series configuration shown below in Figure 2. In such a configuration, the failure of any block will lead to the downing of the system.

Figure 2: Series configuration

### MTBM Calculation

Assume that the operating cycle of the system is 1,000 hours. When a block has failed, it initiates a maintenance action. The system model is simulated for 1,000 hours with 1,000 simulations and Table 1 shows the obtained results.

Table 1: Simulation results for parallel configuration

As an example, Figure 3 shows the Block Up/Down plot for one of the 1,000 simulations that were used to obtain the results shown in the table. You can see that even though blocks B, C and D have failed at different times in the entire operating cycle, the system itself only fails once because of the failure of block D.

Figure 3: Block Up/Down plot for one of the simulations with the parallel configuration

For the MTBM calculation, the system could be rearranged to the series configuration and again simulated with same settings as previously used. Table 2 shows the results of 1,000 simulations with the series configuration.

Table 2: Simulation results for series configuration

Figure 4 shows the Block Up/Down plot for one of the simulations with the series configuration. In this case, you can see that the system was down whenever any component was down.

Figure 4: Block Up/Down plot for one of the simulations with the series configuration

You can calculate the MTBM using the following expression that is based on 1,000 hours and 1,000 simulations for the series configuration.

Based on the MTBM analysis, the average duration in which at least one maintenance action will be required in this system is 461.83 hours. This accounts for all maintenance activities such as scheduled and unscheduled maintenance for the system operation time of 1,000 hours.

## An Easier Approach in BlockSim 8

Although the above method of treating the system as a series configuration in terms of maintainability works, it requires that you recreate the diagram just to calculate the MTBM value. Clearly, this is not efficient, particularly when the system is complex. BlockSim 8 provides a simpler way to do this: when you define the corrective task for each block, you can define that the corrective task will bring the system down.

For each maintenance task, you can specify whether the system will be shut down when the task is performed. For example, as shown in Figure 5, for the corrective task for block B, you can specify under Task Consequences that the task will bring the system down.

Figure 5: Corrective task properties

This property is available for any type of maintenance task (including preventive maintenance, inspections and on-condition inspections). When you change the task consequences in all four blocks in the original parallel RBD shown in Figure 1 and re-simulate, you will see the same results as shown in Table 2.

## Conclusions

Using Mean Time Between Maintenance analysis can help in several ways, including the planning of the maintenance budget and the selection and use of maintenance tasks. In particular, it can help show where the maintenance bottlenecks are and where changes to the maintenance tasks can have their greatest effect.