# Example of Nonparametric Growth Curve

A reliability engineer wants to compare the failure rate for two different types of a brake component that is used on subway trains. The engineer collects replacement time data and component type for 29 trains. Each time a unit failed, it was repaired and returned to service.

The engineer uses a nonparametric growth curve to evaluate the data without assuming a distribution model. For these data, no brake components were retired from service. Therefore, all the data are exact failure times.

1. Open the sample data, BrakeReliability.MTW.
2. Choose Stat > Reliability/Survival > Repairable System Analysis > Nonparametric Growth Curve.
3. In Variables/Start variables, enter Days.
4. Under System Information, select System ID, and then enter ID.
5. Select By variable, and then enter Type.
6. Click OK.

## Interpret the results

Minitab displays nonparametric estimates of the mean cumulative function and its corresponding standard error and confidence limits separately for each group. For example, for the type 1 brake component, the mean cumulative function at 650 days is 1.71429. That is, the mean cumulative number of repairs at 650 days, averaged over all the systems, is approximately 1.7. The engineer can be 95% confident that the true mean cumulative function for the type 1 component at 650 days is contained within the interval 1.27912 and 2.29750.

The engineer uses the mean cumulative difference function to make comparisons across groups. For example, at 500 days, the type 2 brake component had, on average, 2.16420 more failures than the type 1 brake component. The engineer can be 95% confident that, at 500 days, true mean cumulative difference (type 1 – type 2) is contained within the interval −3.23488 and −1.09352.

The event plot shows when the failures occurred for each system. Each line extends to the final day of observation. The plot also shows trends within and across groups. In this plot, system failures generally occur at a constant rate. At 200 days, there are many more failures for the type 2 brake component than the type 1 brake component.

The mean cumulative function plot displays the mean cumulative function for each group. From this plot, the engineer concludes the following:
• The function that represents the type 2 brake component is relatively linear, not curved, up until approximately 450 days. Therefore, the failure rate for the type 2 brake component is relatively constant until 450 days.
• The function that represents the type 1 brake component is linear from approximately 200 days through 700 days, and then increases rapidly. Therefore, the failure rate for the type 1 brake component is fairly constant until 700 days, then increases rapidly.
• The function that represents the type 1 brake component is to the right of the function that represents the type 2 brake component. Therefore, failures occur less often for the type 1 brake component than for the type 2 brake component.
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