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Probabilistic risk analysis using ordered weighted averaging (OWA) operators

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Abstract

The concepts of system load and capacity are pivotal in risk analysis. The complexity in risk analysis increases when the input parameters are either stochastic (aleatory uncertainty) and/or missing (epistemic uncertainty). The aleatory and epistemic uncertainties related to input parameters are handled through simulation-based parametric and non-parametric probabilistic techniques. The complexities increase further when the empirical relationships are not strong enough to derive physical-based models. In this paper, ordered weighted averaging (OWA) operators are proposed to estimate the system load. The risk of failure is estimated by assuming normally distributed reliability index. The proposed methodology for risk analysis is illustrated using an example of nine-input parameters. Sensitivity analyses identified that the risk of failure is dominated by the attitude of a decision-maker to generate OWA weights, missing input parameters and system capacity.

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Notes

  1. In the subsequent sections, the system capacity is assumed a priori known information, either through regulatory guidelines or expert provided data. However, the proposed methods to compute system load is equally applicable

  2. Risk of failure is synonym to probability of failure

Abbreviations

δ:

degree of a polynomial function

α:

degree of orness

Q(r):

linguistic quantifier as a fuzzy subset to generate OWA weights

Q * (r):

linguistic quantifiers “for all” to generate OWA weights

Q * (r):

linguistic quantifiers “there exists” to generate OWA weights

max:

maximum (parameter for uniform distribution)

μ:

mean (normal distribution)

μ Z :

mean of the performance function

μC :

mean of the system capacity

μL :

mean of the system load

s :

measure of scatter (lognormal distribution)

X o :

median (lognormal distribution)

min:

minimum (parameter for uniform distribution)

Φ:

cumulative probability function for a standard normal distribution

w =  (w 1, w 2,...,w n )T :

OWA weight vectors

w j :

OWA weights

Z :

performance function

P f :

probability of system failure

k * :

realizations or iterations in bootstrapping

k :

realizations or iterations in MCS

β:

reliability index

θ:

scale parameter (Weibull distribution)

m w :

shape parameter (Weibull distribution)

σ:

standard deviation (normal distribution)

σ Z :

standard deviation of the performance function

σC :

standard deviation of the system capacity

σL :

standard deviation of the system load

C :

system capacity

L :

system load

b j :

the jth largest element in the vector (X1, X2,..., X n )

\({x^{{k*}}_{1}, x^{{k*}}_{2}, \ldots,x^{{k*}}_{n}}\) :

vector of values for input parameters generated randomly for bootstrapping

\({x^{k}_{1}, x^{k}_{2}, \ldots,x^{k}_{n}}\) :

vector of values for input parameters generated randomly for MCS

F(X i ):

cumulative distribution function

m :

number of historical data points

MCS:

Monte Carlo simulation

n :

number of input parameters

N :

number of realizations in MCS

N * :

number of realizations in bootstrapping

OWA:

ordered weighted averaging

p :

probability of event

P1 and P2 :

parameters of the probability distributions

PDF:

probability density function

X 1, X 2,...,X n :

input parameters

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Authors and Affiliations

  1. Institute for Research in Construction, National Research Council Canada, Ottawa, ON, Canada, K1A 0R6

    Solomon Tesfamariam & Rehan Sadiq

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  1. Solomon Tesfamariam
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  2. Rehan Sadiq
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Correspondence to Solomon Tesfamariam or Rehan Sadiq.

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Tesfamariam, S., Sadiq, R. Probabilistic risk analysis using ordered weighted averaging (OWA) operators. Stoch Environ Res Risk Assess 22, 1–15 (2008). https://doi.org/10.1007/s00477-006-0090-1

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