# Probabilities statistics and rate of failure

Jun 19th, 2019

Probabilities statistics and rate of failure data in literature demand caution even if delving in reputable databases seems to offer a very simple path.

Indeed, one of the cornerstones of risk assessments is assessing probabilities of failure of different components. Classic sources examples are:

- Component Reliability Data for Use in Probabilistic Safety Assessment,” IAEA-TECDOC-478, International Atomic Energy Agency (Oct. 1988), (Link to document) and
- Anon (1991),
*Non-electronic Parts Reliability Data*, RAC Report NPRD, Reliability Analysis Center,Griffiss AFB, NY (Link to document)

A possible approach when using the above-listed references may develop as shown in the examples below.

## Probabilities statistics and rate of failure of a tank example

We start with the case of a tank storage failure rate. The databases report the following:

Based on that mean failure rate estimate the return period (years) is 1/(2.6×10^{-8}/hr*8760 hr./year)=~4400 years.

The mean failure rate appears as 2.6×10^{-8}/hr. (i.e. a very low value). This value likely derives from thee fact that operating experience (last line) showed 136,000 hrs. (15 years) without failures.

This value shows how careful an analyst has to be when using databases results. Indeed, we doubt there is a tank anywhere that has resisted longer than Pyramid of Cheops to the aggression of time and wear. Good sense a little more thinking are necessary to get to a reasonable value leading to a meaningful risk assessment.

## Probabilities statistics and rate of failures, The devil is in the detail

We can now review a pump motor driven failure, using again values from extant reputable databases. Two cases appear in the database in a normal operating environment: the first is “failure to run”, the second is “failure to run given start”.

Pushing a bit further the literature-based approach; we can see below the pump motor driven failure rate probability, but when operated in a heavy chemical environment.

The rate of failure in such an environment is 100 times to a 1000 times greater than the previous example.

One can conclude that taking data at face value is a major blunder, as conditions and peculiarities significantly alter rates of failure.

## Conclusion

As complete statistics are almost never available probabilities can be estimated, using analogies and experience, and “incomplete statistics” from similar subject matters, while recognizing uncertainties and adopting prudent, but reasonable, stances.

Tagged with: Probabilities statistics, rate of failure

Category: Probabilities, Uncategorized

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