SimuMatic

Reliability growth analysis using simulation can be a valuable tool for reliability practitioners. With this approach, reliability growth analyses are performed a large number of times on data sets that have been created using Monte Carlo simulation.

RGA 7's SimuMatic utility generates calculated values of beta and lambda parameters, based on user specified input parameters of beta and lambda. SimuMatic essentially performs a user defined number of Monte Carlo simulations based on user defined required test time or failure termination settings, and then recalculates the beta and lambda parameters for each of the generated data sets. The number of times that the Monte Carlo data sets are generated and the parameters are re-calculated is also user defined. The final output presents the calculated values of beta and lambda and allows for various types of analysis.

To access the SimuMatic utility, either choose Project > Add Other Tools > Add SimuMatic or click the SimuMatic icon on the Project toolbar. For all of the data sets, the basic parameters that are always specified are the beta (β) and lambda (λ) parameters of the Crow-AMSAA (NHPP) model or the Power Law model.

Failure Times

The data set is generated assuming a single system. 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. SimuMatic will return the calculated values of β and λ for a specified number of data sets.

Grouped Failure Times

The data set is generated assuming a single system. 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. In addition, constant or user defined intervals need to be specified for the grouping of the data. SimuMatic will return the calculated values of β and λ for a specified number of data sets.

Multiple Systems - Concurrent

In this case, the number of systems needs to be specified. 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. SimuMatic will return the calculated values of β and λ for a specified number of data sets.

Repairable Systems

Figure 14.5 shows the Main tab of the SimuMatic window where all the necessary user inputs for a multiple systems - concurrent data set have been entered.

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Figure 14.5: The SimuMatic input window

Figure 14.6 shows the generated results based on the input of Figure 14.5. The sorted tab is shown, which allows us to extract conclusions about simulation generated confidence bounds, since the lambda and beta parameters and any other additional output are sorted by percentage. The Analysis tab allows the user to specify the confidence level for simulation generated confidence bounds as shown in Figure 14.7, where simulation confidence bounds are drawn for the cumulative number of failures based on the input parameters specified in Figure 14.5. Extra results based on the calculated lambda and beta parameters can be generated in the Results tab, for example the instantaneous MTBF given a specific test time. This would be calculated as an additional result in addition to the lambda and beta parameters.

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Figure 14.6: SimuMatic output sorted by percentile

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Figure 14.7: Simulation generated confidence bounds on cumulative number of failures

Additional Tools Example 2

A manufacturer wants to design a reliability growth test for a redesigned product, in order to achieve an MTBF of 1,000 hours. Simulation is chosen to estimate the 1-sided 90% confidence bound on the required time to achieve the goal MTBF of 1,000 hours and the 1-sided 90% lower confidence bound on the MTBF at the end of the test time. The total test time is expected to be 15,000 hours. Based on historical data for the previous version, the expected beta and lambda parameters of the test are 0.5 and 0.3, respectively. Do the following:

Generate 1,000 data sets using SimuMatic along with the required output.
Plot the instantaneous MTBF vs. time with the 90% confidence bounds.
Estimate the 1-sided 90% lower confidence bound on time for an MTBF of 1,000 hours.
Estimate the 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test.

Solution to Additional Tools Example 2

Figure 14.8 shows the SimuMatic window with all the appropriate inputs for creating the data sets.

Figure 14.8: The Main tab of the SimuMatic window

Figure 14.9 and Figure 14.10 show the settings in the Analysis and Results tab of the SimuMatic window in order to obtain the desired outputs.

Figure 14.9: The Analysis tab of the SimuMatic window

Figure 14.10: The Results tab of the SimuMatic window

Figure 14.11 displays the results of the simulation. The columns labeled Beta and Lambda contain the different parameters obtained by calculating each data set generated via simulation for the 1,000 data sets. The IMTBF(15,000) column contains the instantaneous MTBF at 15,000 hours (the end of test time) given the parameters obtained by calculating each data set generated via simulation. The Target DMTBF column contains the time required for the MTBF to reach 1,000 hours, given the parameters obtained from the simulation.

Figure 14.11: Simulation results using SimuMatic
Figure 14.12 shows the plot of the instantaneous MTBF with the 90% confidence bounds.

Figure 14.12: Instantaneous MTBF with 90% confidence bounds

The 1-sided 90% lower confidence bound on time assuming MTBF = 1,000 hours can be obtained from the results of the simulation. On the Sorted sheet of the results, this is the target DMTBF value that corresponds to 10.00%, as shown in Figure 14.13. Therefore the 1-sided 90% lower confidence bound on time is 12,642.21 hours.

Figure 14.13: The 1-sided 90% lower confidence bound on time assuming 1,000 hours MTBF

Figure 14.14 shows the 1-sided 90% lower confidence bound on time in the instantaneous MTBF plot. This is indicated by the target lines on the plot.

Figure 14.14: Instantaneous MTBF with the target
The 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test is again obtained from the Sorted sheet of the simulation results by looking at the value in the IMTBF(15,000) column that corresponds to 10.00%. As seen in Figure 14.13, the 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test is 605.93 hours.