Application to FMEA Priority Assessments - Probabilistic Composition of Preferences, Theory and Applications - page 109

Chapter 11
Application to FMEA Priority
Assessments

Abstract A risk priority probability, obtained by multiplying the probabilities of
being the mode of failure of higher risk simultaneously with respect to severity,
occurrence and detectability, is here employed instead of the classical priority risk
number of FMEA. A probabilistic classi

cation of risks with respect to classes

previously determined is also discussed.

Keywords FMEA Risk priority number Risk priority probability Severity

Occurrence Undetectability Ordered classes of risk

11.1 Risk Priority Probabilities

A natural example of the composition of preferences by joint probabilities is the
calculation of priorities of the failure modes in Failure Modes and Effects Analysis

—
FMEA (U.S. Defence Department 1949 ). An important feature of FMEA is the
assignment of a risk priority number (RPN) to each failure mode. To determine that
number, is assigned to each failure mode a score from 1 to 10, or from 1 to 5, with
respect to three features: severity, frequency and detectability. The RPN is simply
obtained by multiplying the values of the scores on these three features.
In Sant Anna ( 2012 ) is proposed the replacement of the RPN by a risk priority

probability (RPP), obtained by multiplying the probabilities of being the mode of
failure of highest risk according to each of these criteria.
This multiplication may be justi

'

ed in terms of probability theory by the com-
bination of conditional probabilities. To evaluate a failure mode, we must rst

consider the likelihood of its cause. Conditionally on the occurrence of such cause,
the evaluation of the risk in the mode of failure must then consider the probability of
such occurrence not being detected in time to avoid its unwanted effects. Finally,
conditionally on occurrence and undetectability is that

the probability of an

undesirable effect should enter the computation.