# 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

### 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

### 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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