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

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 Standard Lower Upper of Failure 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 Standard Lower Upper of Failure 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 Standard Lower Upper of Failure 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 Standard 95.0% Normal CI Time Probability 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 Standard 95.0% Normal CI Time Probability 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 Standard 95.0% Normal CI Time Probability 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.

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