Example for Distribution ID Plot (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 various temperatures. However, some of the units must be removed from the test before they fail. Therefore, the data are right censored. To select a distribution model for the data collected at 80° C, the engineer uses Distribution ID Plot (Right Censoring.

  1. Open the sample data, EngineWindingReliability.MTW.
  2. Choose Stat > Reliability/Survival > Distribution Analysis (Right Censoring) > Distribution ID Plot.
  3. In Variables, enter Temp80.
  4. Select Specify. Ensure that the default distributions are selected (Weibull, Lognormal, Exponential, and Normal).
  5. Click Censor. Under Use censoring columns, enter Cens80.
  6. In Censoring value, type 0.
  7. Click OK in each dialog box.

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.

Distribution ID Plot: Temp80

Goodness-of-Fit Anderson-Darling Distribution (adj) Weibull 68.204 Lognormal 67.800 Exponential 70.871 Normal 68.305
Table of Percentiles Standard 95% Normal CI Distribution Percent Percentile Error Lower Upper Weibull 1 10.0765 2.78453 5.86263 17.3193 Lognormal 1 19.3281 2.83750 14.4953 25.7722 Exponential 1 0.809731 0.133119 0.586684 1.11758 Normal 1 -0.549323 8.37183 -16.9578 15.8592 Weibull 5 20.3592 3.79130 14.1335 29.3273 Lognormal 5 26.9212 3.02621 21.5978 33.5566 Exponential 5 4.13258 0.679391 2.99422 5.70371 Normal 5 18.2289 6.40367 5.67790 30.7798 Weibull 10 27.7750 4.11994 20.7680 37.1463 Lognormal 10 32.1225 3.09409 26.5962 38.7970 Exponential 10 8.48864 1.39552 6.15037 11.7159 Normal 10 28.2394 5.48103 17.4968 38.9820 Weibull 50 62.6158 4.62515 54.1763 72.3700 Lognormal 50 59.8995 4.31085 52.0192 68.9735 Exponential 50 55.8452 9.18089 40.4622 77.0766 Normal 50 63.5518 4.06944 55.5759 71.5278
Table of MTTF Standard 95% Normal CI Distribution Mean Error Lower Upper Weibull 64.9829 4.6102 56.5472 74.677 Lognormal 67.4153 5.5525 57.3656 79.225 Exponential 80.5676 13.2452 58.3746 111.198 Normal 63.5518 4.0694 55.5759 71.528

Distribution ID Plot for Temp80

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