Example of Parametric Distribution Analysis (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. The engineer uses Parametric Distribution Analysis (Arbitrary Censoring) to determine the following:
• The mileage at which various percentages of the mufflers fail
• The percentage of mufflers that will survive past 50,000 miles
• The survival function for the mufflers (as shown on a survival plot)
• The fit of the Weibull distribution for the data (as shown on a probability plot)
1. Open the sample data, MufflerReliability.MTW.
2. Choose Stat > Reliability/Survival > Distribution Analysis (Arbitrary Censoring) > Parametric Distribution Analysis.
3. In Start variables, enter StartOld StartNew.
4. In End variables, enter EndOld EndNew.
5. In Frequency columns (optional), enter FreqOld FreqNew.
6. From Assumed distribution, select Weibull.
7. Click Estimate. In Estimate probabilities for these times (values), enter 50000. Click OK.
8. Click Graphs. Select Survival plot.
9. Click OK in each dialog box.

Interpret the results

Using the Table of Percentiles, the engineer can determine the mileage at which various percentages of the old mufflers and new mufflers fail. For the old mufflers, 10% of the mufflers fail by 38,307 miles. For the new mufflers, 10% of the mufflers to fail by 56,006.1 miles.

Using the Table of Survival Probabilities, the engineer can determine what proportion of the mufflers are expected to survive at least 50,000 miles. For the old mufflers, the probability of surviving past 50,000 miles is approximately 75.07%. For the new mufflers, the probability of surviving past 50,000 miles is approximately 94.67%.

The engineer uses the survival plot to view the survival probabilities at different mileages, and the probability plot to check that the Weibull distribution adequately fits the data.

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