Multiple failure modes analysis (Turnbull estimation method) for Nonparametric Distribution Analysis (Arbitrary Censoring)

In This Topic

Probability of failure – multiple failure modes analysis (Turnbull estimation method)
Probability of survival – multiple failure modes analysis (Turnbull estimation method)

Probability of failure – multiple failure modes analysis (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 majority of failures
Whether the failures are spread among many time intervals or concentrated among a few intervals
Which mode of failure is more prevalent in each interval

Example output

Variable Start: Start End: End

Frequency: Freq

Failure Mode: Failure = Bearing

Turnbull Estimates

Interval		Probability of Failure	Standard Error
Lower	Upper	Probability of Failure	Standard Error
45000	50000	0.060606	0.0293704
55000	60000	0.097179	0.0376876
65000	70000	0.137505	0.0450962
75000	80000	0.108417	0.0417053
85000	90000	0.057706	0.0322684
90000	*	0.538587	*

Variable Start: Start End: End

Frequency: Freq

Failure Mode: Failure = Gasket

Turnbull Estimates

Interval		Probability of Failure	Standard Error
Lower	Upper	Probability of Failure	Standard Error
*	30000	0.037037	0.0209836
30000	40000	0.061728	0.0267402
45000	50000	0.091430	0.0329296
55000	60000	0.057843	0.0280484
65000	70000	0.051270	0.0287739
75000	80000	0.040040	0.0276666
85000	90000	0.044044	0.0303367
90000	*	0.616608	*

Variable Start: Start End: End

Frequency: Freq

Failure Mode: Failure = Bearing, Gasket

Turnbull Estimates

Interval		Probability of Failure	Standard Error
Lower	Upper	Probability of Failure	Standard Error
*	30000	0.037037	0.0209836
30000	40000	0.061728	0.0267402
40000	50000	0.135802	0.0380643
50000	60000	0.123457	0.0365512
60000	70000	0.135802	0.0380643
70000	80000	0.098765	0.0331496
80000	90000	0.061728	0.0267402
90000	*	0.345679	*

Interpretation

For the water pump data:

9.72% (or 0.097179) of the water pumps failed due to bearing problems in the interval from 55,000 to 60,000 miles
5.78% (or 0.057843) of the water pumps failed due to gasket problems in the interval from 55,000 to 60,000 miles
12.35% (or 0.123457) of the water pumps failed for either reason in the interval from 50,000 to 60,000 miles

Probability of survival – multiple failure modes analysis (Turnbull estimation method)

The survival probabilities indicate the probability that a product survives until a particular time. Use the survival probabilities to do the following:

Determine whether your product meets reliability requirements
Compare the reliability of two or more designs of a product

Example output

Variable Start: Start End: End

Frequency: Freq

Failure Mode: Failure = Bearing

Table of Survival Probabilities

	Survival Probability	Standard Error	95.0% Normal CI
Time	Survival Probability	Standard Error	Lower	Upper
50000	0.939394	0.0293704	0.881829	0.996959
60000	0.842215	0.0458749	0.752302	0.932128
70000	0.704711	0.0587451	0.589572	0.819849
80000	0.596294	0.0642532	0.470360	0.722228
90000	0.538587	0.0661109	0.409012	0.668162

Variable Start: Start End: End

Frequency: Freq

Failure Mode: Failure = Gasket

Table of Survival Probabilities

	Survival Probability	Standard Error	95.0% Normal CI
Time	Survival Probability	Standard Error	Lower	Upper
30000	0.962963	0.0209836	0.921836	1.00000
40000	0.901235	0.0331496	0.836262	0.96621
50000	0.809805	0.0442752	0.723027	0.89658
60000	0.751962	0.0496685	0.654613	0.84931
70000	0.700692	0.0543920	0.594085	0.80730
80000	0.660652	0.0581878	0.546606	0.77470
90000	0.616608	0.0620861	0.494922	0.73829

Variable Start: Start End: End

Frequency: Freq

Failure Mode: Failure = Bearing, Gasket

Table of Survival Probabilities

	Survival Probability	Standard Error	95.0% Normal CI
Time	Survival Probability	Standard Error	Lower	Upper
30000	0.962963	0.0209836	0.921836	1.00000
40000	0.901235	0.0331496	0.836262	0.96621
50000	0.765432	0.0470809	0.673155	0.85771
60000	0.641975	0.0532688	0.537570	0.74638
70000	0.506173	0.0555513	0.397294	0.61505
80000	0.407407	0.0545946	0.300404	0.51441
90000	0.345679	0.0528432	0.242108	0.44925

Interpretation

The survival probabilities for each failure mode of the water pump data indicate the following:

84% (or 0.842215) of the water pumps survived without bearing failures for at least 60,000 miles
75% (or 0.751962) of the pumps survived without gasket failures for at least 60,000 miles
64% (or 0.641975) of the pumps survived both failure modes for at least 60,000 miles

To have the greatest impact on improving the reliability of the pumps, the engineers should focus on improving the gaskets.