# Example of Nonparametric 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 Nonparametric Distribution Analysis (Arbitrary Censoring) to determine the probability of failure for various mileage intervals, and to estimate the percentage of mufflers that will survive until at least 50,000 miles. The engineer also wants to validate corresponding results that were obtained using a parametric analysis:

1. Open the sample data, MufflerReliability.MTW.
2. Choose Stat > Reliability/Survival > Distribution Analysis (Arbitrary Censoring) > Nonparametric 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. Click OK.

## Interpret the results

Using the Turnbull Estimates table, the engineer can determine the probability of failure at various mileage intervals. For the old type of mufflers, approximately 19.3% of the mufflers are expected to fail between 50,000 and 60,000 miles. For the new type of mufflers, approximately 10.3% are expected to fail between 50,000 and 60,000 miles.

The engineer can also 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 75.3%. For the new mufflers, the probability of surviving past 50,000 miles is approximately 95.4%. These probabilities are consistent with the results that the engineer obtained using a parametric analysis with a Weibull distribution.

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