# Example of Parametric Distribution Analysis (Right Censoring)

A reliability engineer studies the failure rates of engine windings of turbine assemblies to determine the times at which the windings fail. At high temperatures, the windings might decompose too fast.

The engineer records failure times for the engine windings at 80° C and 100° C. However, some of the units must be removed from the test before they fail. Therefore, the data are right censored. The engineer uses Parametric Distribution Analysis (Right Censoring) to determine the following:
• The times at which various percentages of the windings fail. The engineer is particularly interested in the 0.1th percentile
• The percentage of windings that will survive past 70 hours
• The survival function for the engine windings (as shown on a survival plot)
• The fit of the lognormal distribution for the data (as shown on a probability plot)
1. Open the sample data, EngineWindingReliability.MTW.
2. Choose Stat > Reliability/Survival > Distribution Analysis (Right Censoring) > Parametric Distribution Analysis.
3. In Variables, enter Temp80 Temp100.
4. From Assumed distribution, select Lognormal.
5. Click Censor. Under Use censoring columns, enter Cens80 Cens100.
6. In Censoring value, type 0. Click OK.
7. Click Estimate. In Estimate percentiles for these additional percents, enter 0.1.
8. In Estimate probabilities for these times (values), enter 70. Click OK.
9. Click Graphs. Select Survival plot.
10. Click OK in each dialog box.

## Interpret the results

Using the Table of Percentiles, the engineer can determine the times at which various percentages of the windings fail. At 80° C, 1% of the windings to fail by 19.3281 hours. The values for the 0.1th percentile, which the engineer requested for the analysis, are also shown in the table. At 80° C, 0.1% of the windings fail by 13.3317 hours. At 100° C, 0.1% of the windings fail by 3.93505 hours. Therefore, the increase in temperature decreases the percentile by a value of approximately 9.5 hours.

Using the Table of Survival Probabilities, the engineer can determine what proportion of windings are expected to survive for more than 70 hours. At 80° C, 37.43% of the windings are expected to survive for more than 70 hours. At 100° C, 19.82% of the windings are expected to survive for more than 70 hours.

The engineer uses the survival plot to view the survival probabilities over time, and the probability plot to check that the lognormal distribution adequately fits the data.

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