Actuarial estimation method for Nonparametric Distribution Analysis (Arbitrary 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. 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 Error	95.0% Normal CI
Median	Standard 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 Units
		Additional Time	Standard Error	95.0% Normal CI
Time T		Additional Time	Standard 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 Probability of Failure
Interval		Number Entering	Number Failed	Number Censored		Standard Error
Lower	Upper	Number Entering	Number Failed	Number Censored		Standard 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 Probability	Standard Error	95.0% Normal CI
Time	Survival Probability	Standard 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.