Hazard and density estimates for Nonparametric Distribution Analysis (Right Censoring)

Hazard estimates – actuarial estimation method

The hazard function provides a measure of the likelihood of failure as a function of how long the unit has survived (the instantaneous failure rate at a particular time, t).

Although the nonparametric hazard function is not dependent on any specific distribution, you can use it to help determine which distribution might be appropriate for modeling the data if you decide to use parametric estimation methods. Select a distribution that has a hazard function that resembles the nonparametric hazard function.

Interpretation

For engine windings that run at 80° C, the likelihood of failure is approximately 3.07 (0.0266667/0.0086957) times greater after 70 hours than after 30 hours.

Density estimates – actuarial estimation method

The density estimates describe the distribution of failure times and provide a measure of the likelihood that a product fails at particular times.

Although the nonparametric density function is not dependent on any specific distribution, you can use it to help determine which distribution might be appropriate for modeling the data if you decide to use a parametric estimation methods. Select a distribution that has a density function that resembles the nonparametric density function.

Interpretation

For engine windings running at 80° C, the likelihood of failure is greater at 50 hours (0.021000) than at 70 hours (0.0088421).

Comparison of survival curves – actuarial estimation method

Use the log-rank and Wilcoxon tests to compare the survival curves of two or more data sets. Each test detects different types of differences between the survival curves. Therefore, use both tests to determine whether the survival curves are equal.

The log-rank test compares the actual and expected number of failures between the survival curves at each failure time.

The Wilcoxon test is a log-rank test that is weighted by the number of items that still survive at each point in time. Therefore, the Wilcoxon test weights early failure times more heavily.

Interpretation

For the engine windings data, the test is to determine whether the survival curves for the engine windings running at 80° C and 100° C are different. Because the p-value for both tests is less than an α-value of 0.05, the engineer concludes that a significant difference exists between the survival curves.

By using this site you agree to the use of cookies for analytics and personalized content.  Read our policy