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.

Example output

Characteristics of Variable Standard 95.0% Normal CI Median Error Lower Upper 77260.5 620.465 76044.4 78476.6

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.

Example output

Additional Time from Time T until 50% of Running Units Fail Proportion of Running Additional Standard 95.0% Normal CI Time T Units Time Error Lower Upper 20000 1.00000 57260.5 620.465 56044.4 58476.6 30000 0.99714 47318.0 619.577 46103.7 48532.4 40000 0.98665 37528.7 616.311 36320.8 38736.7 50000 0.95424 28180.1 606.103 26992.1 29368.0 60000 0.85129 20267.5 614.879 19062.3 21472.6 70000 0.68065 13950.6 549.810 12873.0 15028.2 80000 0.43184 9321.0 437.938 8462.6 10179.3

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.

Example output

Actuarial Table Conditional Interval Number Number Number Probability Standard Lower Upper Entering Failed Censored of Failure Error 0 20000 1049 0 0 0.000000 0.0000000 20000 30000 1049 3 0 0.002860 0.0016488 30000 40000 1046 11 0 0.010516 0.0031541 40000 50000 1035 34 0 0.032850 0.0055405 50000 60000 1001 108 0 0.107892 0.0098059 60000 70000 893 179 0 0.200448 0.0133967 70000 80000 714 261 0 0.365546 0.0180228 80000 90000 453 243 0 0.536424 0.0234296

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.

Example output

Table of Survival Probabilities Survival Standard 95.0% Normal CI Time Probability Error Lower Upper 20000 1.00000 0.0000000 1.00000 1.00000 30000 0.99714 0.0016488 0.99391 1.00000 40000 0.98665 0.0035430 0.97971 0.99360 50000 0.95424 0.0064517 0.94160 0.96689 60000 0.85129 0.0109856 0.82976 0.87282 70000 0.68065 0.0143949 0.65243 0.70886 80000 0.43184 0.0152936 0.40186 0.46181 90000 0.20019 0.0123546 0.17598 0.22441

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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