Application to FMEA Priority Assessments - Probabilistic Composition of Preferences, Theory and Applications - page 113

failures, do not come from uni ed processes, but from application of personal value

systems, the treatment of uncertainty becomes even more dif cult.

cations to FMEA practice have been proposed to account for uncertainty.
Unsatisfactory results of the application of these proposals can be attributed to the
direct form of composition of the speci

Modi

c indices rather than to the account of the
uncertainty taken in the calculation of these speci c indices (Jin 2000 ; Lee 2001 ).

An often explored option is the use of fuzzy logic (Zadeh 1978 ) in the combi-
nation of the indices, whether or not these criteria are measured by fuzzy numbers
(Bowles and Pelaez 1995 ; Pillay and Wang 2003 ). This form of composition results
in prioritizing maximum or minimum values, disregarding the intermediate ones.
The use of the product, on the contrary, by considering all the values, provides
greater robustness to the final outcome of FMEA.

Other proposed changes are based on standardizing the values by dividing by the
amplitude observed in each index, to correct for the different variability in the three
components (Tay and Lim 2006 ; Keskin and Ozkan 2009 ). This may result in
neglecting the information provided by this variability, allowing for distortions
even more dif final outcome than those resulting from the

direct multiplication of the original values.
The transformation into probabilities of preference and the probabilistic com-
position by the product of the probabilities provide greater security to handle the
uncertainty in each factor and the differences in variability in the evaluations of the
different risk factors.

cult to identify in the

11.4 Practical Considerations

An example of modeling uncertainty is given by the analysis in Sant Anna et al.

( 2014 ) of the data of Chuang ( 2010 ) about 23 modes of failures in the services of a
hypermarket. That is a typical case of the service sector, where scales of equally
spaced values are employed with the identi

'

cation of the importance levels in the

scale left open to the evaluators.
The importance of the modes of failure according to the three FMEA criteria was
determined in the study of Chuang ( 2010 ) by averages of evaluations by a team of
100 specialists. This approach allows for statistically estimating the dispersion in
the evaluations according to each criterion. For instance, an estimator for the range
of the distributions related to severity may be derived from the vector of 23 sample
ranges observed in the 23 sets of 100 evaluations of each mode of failure according
to severity.
Alternatively, the information on the dispersion within the samples of 100
evaluations may be left out of consideration to employ, instead, the variation of the
means of such samples along the 23 modes of failure. It can be argued that the
variation along the set of specialists does not correctly inform on the uncertainty in
the application of the criterion, as all of them may be not equally affected by this
uncertainty. The variability observed along the evaluations of the different modes of