# Kaplan-Meier estimation method for Nonparametric Distribution Analysis (Right Censoring)

## Characteristics of Variable – Kaplan-Meier estimation method

The MTTF (mean time to failure) and the median are measures of the center of the distribution. The IQR is a measure of the spread of the distribution.

### Interpretation

The characteristics of the variable are shown for the engine windings that are tested at 80° C.

The MTTF (63.7123) is a sensitive statistic because outliers and the tails in a skewed distribution significantly affect its values.

The median (55) and the IQR are resistant statistics because the tails in a skewed distribution and outliers do not significantly affect their values.
###### Note

In this example, due to censoring, there is not sufficient failure data to calculate where 75% fail or 25% survive (Q3). Therefore, Minitab displays a missing value * for Q3 and IQR.

## Kaplan-Meier Estimates – Kaplan-Meier estimation method

The survival probabilities indicate the probability that the product survives until a particular time. Use these values to determine whether your product meets reliability requirements or to compare the reliability of two or more designs of a product.

Nonparametric estimates do not depend on any particular distribution and therefore are good to use when no distribution adequately fits the data.

### Interpretation

For the engine windings tested at 80° C, 0.42, or 42%, of the windings survived for at least 60.0 hours.

## Empirical hazard function – Kaplan-Meier estimation method

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

The empirical hazard function always results in an increasing function; therefore, the likelihood of failure is assumed to increase as a function of age.

### Interpretation

For the engine windings tested at 80° C, the likelihood of failure is 2 (0.0500000/0.0250000) times greater after the windings run for 61 hours than after the windings run for 45 hours.

## Comparison of survival curves – Kaplan-Meier 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 the same. 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.

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