Actuarial estimation method for Nonparametric Distribution Analysis (Right Censoring)

In This Topic

Characteristics of variable – actuarial estimation method
Additional time from Time T until 50% of running units fail – actuarial estimation method
Conditional probability of failure – actuarial estimation method
Survival probabilities – actuarial estimation method

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 Error	95.0% Normal CI
Median	Standard Error	Lower	Upper
56.1905	3.36718	49.5909	62.7900

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

Additional Time from Time T until 50% of Running Units Fail

	Proportion of Running Units
		Additional Time	Standard Error	95.0% Normal CI
Time T		Additional Time	Standard 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

Interpretation

For the engine windings at 80° C, 84% of the windings survive until 40 hours. After an estimated 20 more hours, an additional 50% 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

Actuarial Table

					Conditional Probability of Failure
Interval		Number Entering	Number Failed	Number Censored		Standard Error
Lower	Upper	Number Entering	Number Failed	Number Censored		Standard 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

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

Table of Survival Probabilities

	Survival Probability	Standard Error	95.0% Normal CI
Time	Survival Probability	Standard 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

Interpretation

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