# An Improved Framework for Uncertainty Analysis: Accounting for Unsuspected Errors

## Alexander I. Shlyakhter

*Risk Analysis*, **14**(4): 441-447, 1994

## Abstract

I use an analogy with the history of physical measurements, population and energy projections,
and analyze the trends in several data sets to quantify the overconfidence of the experts in the
reliability of their uncertainty estimates. Data sets include (i) time trends in the sequential measurements
of the same physical quantity; (ii) national population projections; and (iii) projections
for the US., energy sector. Probabilities of large deviations for the true values are parametrized
by an exponential distribution with the slope determined by the data. Statistics of past errors can
be used in probabilistic risk assessment to hedge against unsuspected uncertainties and to include
the possibility of human error into the framework of uncertainty analysis. By means of a sample
Monte Carlo simulation of cancer risk caused by ingestion of benzene in soil, I demonstrate how
the upper 95th percentiles of risk are changed when unsuspected uncertainties are included. I
recommend to inflate the estimated uncertainties by default safety factors determined from the
relevant historical data sets.

### Keywords: Uncertainty analysis; physical measurements; population projections; energy projections;
Monte Carlo simulations.

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