 Reliability Basics

# Using SimuMatic in RGA

Simulation is a very powerful tool that can assist with developing test plans or generating bootstrap confidence intervals. This article will describe the function of SimuMatic in RGA and provide an example of how SimuMatic can be used to determine the sample size that is needed to demonstrate a reliability goal at a specified confidence level.

## SimuMatic

RGA's SimuMatic utility uses Monte Carlo simulation to generate a specified number of data sets based on user-specified inputs and then automatically calculates the beta and lambda parameters of the Crow-AMSAA model for each of the generated sets. Using this type of an analysis, one can estimate the expected confidence bounds on the demonstrated MTBF or failure intensity at the end of the test, and one can determine whether the planned test time or sample size will suffice to achieve a goal MTBF at the end of a test.

The data types that can be generated using SimuMatic are described next. With each data type, there is a choice between a time-terminated test, where the termination time needs to be specified, or a failure-terminated test, where the number of failures needs to be specified.

• Failure Times: The data sets are generated assuming a single system.
• Multiple Systems – Concurrent: The number of systems needs to be specified.
• Grouped Failure Times: The data sets are generated assuming a single system. Constant or user-defined intervals need to be specified for the grouping of the data.
• Repairable Systems: The number of systems needs to be specified.

## Example

A reliability engineer is developing a reliability growth test plan for a new system. The target MTBF that she needs to demonstrate at the end of the test is 800 hours with a 90% confidence. She has been allocated 2,000 hours of test time and wants to determine how many prototypes will need to be tested in order to demonstrate the MTBF goal. From historical growth tests on previous design iterations of the system, she estimates that the beta and lambda parameters of the Crow-AMSAA model are expected to be 0.55 and 0.21, respectively.

The reliability engineer decided to use the SimuMatic tool in RGA in order to design the reliability growth test. Figure 1 shows the Main tab of SimuMatic’s setup window. Figure 1: Main tab of the SimuMatic setup window

The estimated Crow-AMSAA parameters were entered and the data type that was chosen was Multiple Systems – Concurrent, since the test will include more than one system. The test was set to end at 2,000 hours, which is the current time constraint. 10 systems were initially selected to be used in the test. Finally, 1,000 simulations were chosen to be run.

Figure 2 shows the remaining tabs of the SimuMatic window, where the engineer chose to calculate the upper 1-sided 90% confidence bound on the time required to reach the target MTBF of 800 hours (entered in the window as the lower 1-sided 10% confidence bound). She also chose to calculate the demonstrated MTBF at the end of the test. Figure 2: Remaining tabs of the SimuMatic setup window

Using these settings, SimuMatic generated 1,000 data sets and automatically calculated beta and lambda for each set. Figure 3 shows a portion of the calculated parameters and results of the analysis arranged in an ascending order based on the Percentage column. This column indicates the percentage of values that are less than or equal to each corresponding value. The lower 1-sided 90% confidence bound on the demonstrated MTBF at the end of the test can be found by looking at the value under the DMTBF column that corresponds to the 10th percentile (the upper 1-sided 90% bound would be the value that corresponds to the 90th percentile). As it can be seen from the highlighted row, the demonstrated MTBF at the end of the test is 668.123 hours. Figure 3: Lower 1-sided 90% bound on the demonstrated MTBF

Given that the target MTBF has not been met at the end of the test, the next step is to determine the required time to reach that goal. The required time is displayed in the “Target DMTBF” column in the SimuMatic results. Figure 4 shows the highlighted row that gives the upper 1-sided 90% confidence bound on the time required to reach the target MTBF of 800 hours. Note that the upper bound was used in this case because it corresponds to the worst case scenario of time required to reach the target. Figure 4: Upper 1-sided 90% bound on time to reach the target MTBF

As it can be seen, the required time to reach the target MTBF is 28,292 hours. The same value can be confirmed by looking at the Instantaneous MTBF vs. Time plot as shown in Figure 5. Figure 5: Instantaneous MTBF vs. Time plot

Given that each system in the test accumulates 2,000 hours of testing, the current plan of 10 systems will lead to a total accumulated time of 20,000 hours. Therefore, approximately 10,000 hours of additional test time are required in order to accumulate 28,292 test hours and reach the target MTBF. In other words, an additional 5 systems (each tested for 2,000 hours) will be needed to accumulate enough test time.

Figure 6 shows the results of another simulation, where the number of systems in the test was set to 15 instead of 10. The lower 1-sided 90% confidence bound on the demonstrated MTBF at the end of the test can be found by looking at the value under the DMTBF column that corresponds to the 10th percentile. That value is 837.3306 hours. Figure 6: Lower 1-sided 90% bound on the demonstrated MTBF with 15 systems in the test

As these results show, if 15 systems are included in the test and each one is tested for 2,000 hours, then the goal MTBF of 800 hours with a 90% confidence should be met.

## Conclusion

This article illustrated how Monte Carlo simulation and the SimuMatic tool in RGA can be used to determine whether a given test plan will demonstrate an MTBF goal at a specified confidence level. If a plan won't demonstrate the goal, the article illustrated how SimuMatic can be used to modify the plan so that it will. As with any test design, the inputs to the design (the beta and lambda parameters of the Crow-AMSAA in this case) will have a great effect on the calculated results and oftentimes need to be assumed. Nevertheless, SimuMatic can be very useful for obtaining an estimate of required test time or sample size. 