Actuarial estimation method for Nonparametric Distribution Analysis (Right Censoring)

Characteristics of variable – actuarial estimation method

The median is a measure of the center of the distribution.

Nonparametric estimates do not depend on any particular distribution. Therefore, these estimates are useful when no distribution adequately fits the data.

Example output

Characteristics of Variable Standard 95.0% Normal CI Mean(MTTF) Error Lower Upper Q1 Median Q3 IQR 63.7123 3.83453 56.1968 71.2279 48 55 * *

Interpretation

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

The median (56.1905) is a resistant statistic because outliers and the tails in a skewed distribution do not significantly affect its values.

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

Kaplan-Meier Estimates Number Number Survival Standard 95.0% Normal CI Time at Risk Failed Probability Error Lower Upper 23 50 1 0.980000 0.0197990 0.941195 1.00000 24 49 1 0.960000 0.0277128 0.905684 1.00000 27 48 2 0.920000 0.0383667 0.844803 0.99520 31 46 1 0.900000 0.0424264 0.816846 0.98315 34 45 1 0.880000 0.0459565 0.789927 0.97007 35 44 1 0.860000 0.0490714 0.763822 0.95618 37 43 1 0.840000 0.0518459 0.738384 0.94162 40 42 1 0.820000 0.0543323 0.713511 0.92649 41 41 1 0.800000 0.0565685 0.689128 0.91087 45 40 1 0.780000 0.0585833 0.665179 0.89482 46 39 1 0.760000 0.0603987 0.641621 0.87838 48 38 3 0.700000 0.0648074 0.572980 0.82702 49 35 1 0.680000 0.0659697 0.550702 0.80930 50 34 1 0.660000 0.0669925 0.528697 0.79130 51 33 4 0.580000 0.0697997 0.443195 0.71680 52 29 1 0.560000 0.0701997 0.422411 0.69759 53 28 1 0.540000 0.0704840 0.401854 0.67815 54 27 1 0.520000 0.0706541 0.381521 0.65848 55 26 1 0.500000 0.0707107 0.361410 0.63859 56 25 1 0.480000 0.0706541 0.341521 0.61848 58 24 2 0.440000 0.0701997 0.302411 0.57759 59 22 1 0.420000 0.0697997 0.283195 0.55680 60 21 1 0.400000 0.0692820 0.264210 0.53579 61 20 1 0.380000 0.0686440 0.245460 0.51454 62 19 1 0.360000 0.0678823 0.226953 0.49305 64 18 1 0.340000 0.0669925 0.208697 0.47130 66 17 1 0.320000 0.0659697 0.190702 0.44930 67 16 2 0.280000 0.0634980 0.155546 0.40445 74 13 1 0.258462 0.0621592 0.136632 0.38029

Interpretation

For the engine windings at 80° C, 84% of the windings survive until 40 hours. After an estimated 20 more hours, an additional 42% ((0.84 x 0.5) x 100) of the windings that are still running at 40 hours 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

Empirical Hazard Function Hazard Time Estimates 23 0.0200000 24 0.0204082 27 0.0212766 31 0.0217391 34 0.0222222 35 0.0227273 37 0.0232558 40 0.0238095 41 0.0243902 45 0.0250000 46 0.0256410 48 0.0277778 49 0.0285714 50 0.0294118 51 0.0333333 52 0.0344828 53 0.0357143 54 0.0370370 55 0.0384615 56 0.0400000 58 0.0434783 59 0.0454545 60 0.0476190 61 0.0500000 62 0.0526316 64 0.0555556 66 0.0588235 67 0.0666667 74 0.0769231

Interpretation

At 80° C, an engine winding that survived until 40 hours has a probability of 0.500000 (or a 50% chance) of failing in the interval of 40 to 60 hours.

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

Distribution Analysis: Temp80

Variable: Temp80

Censoring Censoring Information Count Uncensored value 37 Right censored value 13 Censoring value: Cens80 = 0

Nonparametric Estimates

Characteristics of Variable Standard 95.0% Normal CI Median Error Lower Upper 56.1905 3.36718 49.5909 62.7900
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 20 1.00 36.1905 3.36718 29.5909 42.7900 40 0.84 20.0000 3.08607 13.9514 26.0486
Actuarial Table Conditional Interval Number Number Number Probability Standard Lower Upper Entering Failed Censored of Failure Error 0 20 50 0 0 0.000000 0.000000 20 40 50 8 0 0.160000 0.051846 40 60 42 21 0 0.500000 0.077152 60 80 21 8 4 0.421053 0.113269 80 100 9 0 6 0.000000 0.000000 100 120 3 0 3 0.000000 0.000000
Table of Survival Probabilities Survival Standard 95.0% Normal CI Time Probability Error Lower Upper 20 1.00000 0.0000000 1.00000 1.00000 40 0.84000 0.0518459 0.73838 0.94162 60 0.42000 0.0697997 0.28320 0.55680 80 0.24316 0.0624194 0.12082 0.36550 100 0.24316 0.0624194 0.12082 0.36550 120 0.24316 0.0624194 0.12082 0.36550
Hazards and Densities Hazard Standard Density Standard Time Estimates Error Estimates Error 10 0.0000000 * 0.0000000 * 30 0.0086957 0.0030627 0.0080000 0.0025923 50 0.0333333 0.0068579 0.0210000 0.0034900 70 0.0266667 0.0090867 0.0088421 0.0027959 90 0.0000000 * 0.0000000 * 110 0.0000000 * 0.0000000 *

Interpretation

At 80° C, 0.84, or 84%, of the engine windings survived at least 40 hours.

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