Turnbull estimation method for Nonparametric Distribution Analysis (Arbitrary Censoring)

In This Topic

Probability of failure – Turnbull estimation method
Survival probabilities – Turnbull estimation method

Probability of failure – Turnbull estimation method

The probability of failure provides, for each interval, the chance that the product will fail in that interval. Use this information to determine the following:

Which intervals have the most failures
Whether the failures are spread among many time intervals or concentrated among a few intervals

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

Example output

Turnbull Estimates

Interval		Probability of Failure	Standard Error
Lower	Upper	Probability of Failure	Standard Error
20000	30000	0.002860	0.0016488
30000	40000	0.010486	0.0031451
40000	50000	0.032412	0.0054678
50000	60000	0.102955	0.0093830
60000	70000	0.170639	0.0116151
70000	80000	0.248808	0.0133481
80000	90000	0.231649	0.0130259
90000	*	0.200191	*

Interpretation

For the new muffler data, 0.248808 (or 24.8808%) of the new type of mufflers failed in the interval from 70,000 to 80,000 miles.

Survival probabilities – Turnbull estimation method

The survival probabilities indicate the probability 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
30000	0.997140	0.0016488	0.993909	1.00000
40000	0.986654	0.0035430	0.979710	0.99360
50000	0.954242	0.0064517	0.941597	0.96689
60000	0.851287	0.0109856	0.829756	0.87282
70000	0.680648	0.0143949	0.652435	0.70886
80000	0.431840	0.0152936	0.401865	0.46181
90000	0.200191	0.0123546	0.175976	0.22441

Interpretation

For the new muffler data, 0.954242 (or 95.4242%) of the new type of mufflers survive at least 50,000 miles.