# Actuarial estimation method for Nonparametric Distribution Analysis (Arbitrary Censoring)

## Characteristics of variable – actuarial estimation method

The median is a measure of the center of the distribution. The median is a resistant statistic because outliers and the tails in a skewed distribution do not significantly affect its value.

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

### Interpretation

The median is 77,260.5.

## Additional time from Time T until 50% of running units fail – actuarial estimation method

Use the additional time table to determine how much additional time, from a fixed time, passes before a certain percentage of the currently surviving products will fail. For each "Time T", Minitab estimates the additional time that must pass until one-half of the currently surviving products fail.

### Interpretation

For the new muffler data, at 50,000 miles, 0.95424 of the new type of mufflers are still running. After an estimated 28,180.1 more miles, an additional 47.71% ((0.95424 x 0.5) x 100) of the mufflers that are still running at 50,000 miles are expected to fail.

## Conditional probability of failure – actuarial estimation method

The conditional probability of failure indicates the probability that a product that has survived until the beginning of a particular interval will fail within the interval.

### Interpretation

For the new muffler data, a muffler that survived until 50,000 miles has a probability of 0.107892 (or a 10.7892% chance) of failing in the interval of 50,000 to 60,000 miles.

## Survival probabilities – actuarial 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.

### Interpretation

For the new muffler data, 0.95424 (or 95.424%) of the new type of mufflers survive at least 50,000 miles.

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