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 various temperatures. However, some of the units do not fail before the test ends. Therefore, the data are right censored. To select a distribution model for the data collected at 80° C, the engineer uses Distribution ID Plot.
- Open the sample data, EngineWindingReliability.MWX.
- Choose .
- From Censoring, select Right censored data with censoring column.
- From Data, select One or more samples, each in a column.
- In Sample column, enter Temp80.
- In Censoring column, enter Cens80.
- In Censoring value, select 0.
-
Deselect Location scale distributions and Distributions with a threshold parameter to assess the following distributions:
- Weibull
- Lognormal
- Loglogistic
- Exponential
- Select OK.
Interpret the results
The points for the failure times fall approximately on the straight line on the lognormal probability plot. Therefore, the lognormal distribution provides a good fit. The engineer thus decides to use the lognormal distribution to model the data collected at 80° C.
Minitab also displays a table of percentiles and a table of mean time to failure (MTTF), which provide calculated failure times for each distribution. You can compare the calculated values to see how your conclusions may change with different distributions. If several distributions fit your data well, you may want to use the distribution that provides the most conservative results.
Tip
The analysis stores a reliability data definition that includes the sample columns and the censoring scheme. Select the definition to quickly run Distribution ID Plot, Distribution Overview Plot, Parametric Distribution Analysis, and Nonparametric Distribution Analysis on the same data.
Goodness-of-Fit
| Distribution | Anderson-Darling (adj) |
|---|---|
| Weibull | 68.204 |
| Lognormal | 67.800 |
| Loglogistic | 67.721 |
| Exponential | 70.871 |
Table of Percentiles
| Standard Error | 95% Normal CI | ||||
|---|---|---|---|---|---|
| Distribution | Percent | Percentile | Lower | Upper | |
| Weibull | 1 | 10.0765 | 2.78453 | 5.86263 | 17.3193 |
| Lognormal | 1 | 19.3281 | 2.83750 | 14.4953 | 25.7722 |
| Loglogistic | 1 | 16.0857 | 2.99498 | 11.1675 | 23.1699 |
| Exponential | 1 | 0.809731 | 0.133119 | 0.586684 | 1.11758 |
| Weibull | 5 | 20.3592 | 3.79130 | 14.1335 | 29.3273 |
| Lognormal | 5 | 26.9212 | 3.02621 | 21.5978 | 33.5566 |
| Loglogistic | 5 | 25.5948 | 3.27675 | 19.9149 | 32.8947 |
| Exponential | 5 | 4.13258 | 0.679391 | 2.99422 | 5.70371 |
| Weibull | 10 | 27.7750 | 4.11994 | 20.7680 | 37.1463 |
| Lognormal | 10 | 32.1225 | 3.09409 | 26.5962 | 38.7970 |
| Loglogistic | 10 | 31.5836 | 3.29780 | 25.7385 | 38.7560 |
| Exponential | 10 | 8.48864 | 1.39552 | 6.15037 | 11.7159 |
| Weibull | 50 | 62.6158 | 4.62515 | 54.1763 | 72.3700 |
| Lognormal | 50 | 59.8995 | 4.31085 | 52.0192 | 68.9735 |
| Loglogistic | 50 | 58.6087 | 4.07051 | 51.1498 | 67.1552 |
| Exponential | 50 | 55.8452 | 9.18089 | 40.4622 | 77.0766 |
Table of MTTF
| Standard Error | 95% Normal CI | |||
|---|---|---|---|---|
| Distribution | Mean | Lower | Upper | |
| Weibull | 64.9829 | 4.6102 | 56.5472 | 74.677 |
| Lognormal | 67.4153 | 5.5525 | 57.3656 | 79.225 |
| Loglogistic | 66.9996 | 5.5835 | 56.9031 | 78.887 |
| Exponential | 80.5676 | 13.2452 | 58.3746 | 111.198 |
