Example for Distribution ID Plot (Arbitrary Censoring)

A reliability engineer wants to assess the reliability of a new type of muffler and to estimate the proportion of warranty claims that can be expected with a 50,000-mile warranty. The engineer collects failure data on both the old type and the new type of mufflers. Mufflers were inspected for failure every 10,000 miles.

The engineer records the number of failures for each 10,000-mile interval. Therefore, the data are arbitrarily censored. Before analyzing the failure data for the new mufflers using Parametric Distribution Analysis (Arbitrary Censoring), the engineer uses Distribution ID Plot (Arbitrary Censoring) to select a distribution model for the analysis.

  1. Open the sample data, MufflerReliability.MTW.
  2. Choose Stat > Reliability/Survival > Distribution Analysis (Arbitrary Censoring) > Distribution ID Plot.
  3. In Start variables, enter StartNew.
  4. In End variables, enter EndNew.
  5. In Frequency columns (optional), enter FreqNew.
  6. Select Specify. Ensure that the default distributions are selected (Weibull, Lognormal, Exponential, and Normal).
  7. Click OK.

Interpret the results

On the Weibull probability plot, the points fall approximately on the straight line. Therefore, the Weibull distribution provides a good fit. The engineer thus decides to use the Weibull distribution to model the data for Parametric Distribution Analysis (Arbitrary Censoring).

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: Start = StartNew and End = EndNew

Using frequencies in FreqNew

Goodness-of-Fit Anderson-Darling Distribution (adj) Weibull 7.278 Lognormal 7.322 Exponential 8.305 Normal 7.291
Table of Percentiles Standard 95% Normal CI Distribution Percent Percentile Error Lower Upper Weibull 1 37265.1 938.485 35470.3 39150.6 Lognormal 1 43817.7 688.033 42489.7 45187.2 Exponential 1 941.789 32.5296 880.143 1007.75 Normal 1 39810.3 1047.34 37757.6 41863.1 Weibull 5 49434.9 841.147 47813.5 51111.3 Lognormal 5 51458.9 624.451 50249.5 52697.5 Exponential 5 4806.55 166.019 4491.93 5143.21 Normal 5 50694.9 810.524 49106.3 52283.5 Weibull 10 56006.1 759.186 54537.7 57514.0 Lognormal 10 56063.1 585.905 54926.4 57223.3 Exponential 10 9873.05 341.017 9226.79 10564.6 Normal 10 56497.5 699.183 55127.1 57867.8 Weibull 50 77639.9 501.312 76663.5 78628.7 Lognormal 50 75850.3 576.625 74728.5 76988.9 Exponential 50 64952.9 2243.49 60701.3 69502.3 Normal 50 76966.0 514.756 75957.1 77974.9
Table of MTTF Standard 95% Normal CI Distribution Mean Error Lower Upper Weibull 76585.0 488.71 75633.1 77549 Lognormal 77989.9 615.96 76792.0 79207 Exponential 93707.3 3236.67 87573.5 100271 Normal 76966.0 514.76 75957.1 77975

Distribution ID Plot for StartNew

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