International Journal of Computer Applications (0975 – 8887) Volume 44– No17, April 2012 16 Sensitivity Analysis in Radiological Risk Assessment using Double Monte Carlo Method Hrishikesh Boruah, Dept. of Mathematics, Dibrugarh University, Dibrugarh-786004, India. Tazid Ali, Dept. of Mathematics, Dibrugarh University, Dibrugarh-786004, India. Palash Dutta Dept. of Mathematics, Dibrugarh University, Dibrugarh-786004, India ABSTRACT Sensitivity analysis is a study of how changes in the inputs to a model influence the results of the model. Many techniques are available when the model is probabilistic. In this paper we consider a related problem of sensitivity analysis when the model includes uncertain variable that can involve both aleatory and epistemic uncertainty and the method of calculation is Probability bounds analysis. In this study, an advanced probabilistic technique called the Double Monte Carlo method is applied to estimate the radiological risk due to SR-90 through ingestion of food items. The variables of the risk model along with the parameters of these variables are described in terms of probability distribution (precise and imprecise). Keywords: Uncertainty, Risk Assessment, Double Monte Carlo, Sensitivity Analysis. 1. INTRODUCTION The Greek in the 4 th century BC were the first recorded civilization to have considered uncertainty. Uncertainty plays a critical role in the analysis for a wide and diverse set in various fields. Ideals and concepts of uncertainty have long been associated with gambling and games. There are two kinds of uncertainty [7]. The first kind called aleatory uncertainty arises due to randomness and the other called epistemic uncertainty arises due to lack of data or insufficient information. These two kinds of Uncertainty can propagate through various mathematical expressions with different calculation method. Probabilistic risk assessment (PRA) is related to one of these methods. Probabilistic risk assessment (PRA) applies the probability distribution for the input variables of the risk assessment model in order to quantitatively characterize their variabilities and uncertainties. Two interpretations are generally proposed [4] for the distribution of the input variable. First, Uncertainty regarding variability may be viewed in terms of probability regarding frequencies. Secondly variability is described by frequency distributions, and that uncertainty in general, including sampling error, measurement error, and estimates based upon judgment, is described by probability distribution. The most widely used method in PRA is Monte Carlo analysis (MCA), which is a means of quantifying uncertainty or variability in a probability framework using computer simulation. When inputs are tainted with both kinds of uncertainty, then an advanced modeling approach called Two-dimensional Monte Carlo analysis (2D MCA) can be used. 2. PROBABILITY BOUNDS AS A SENSITIVITY ANALYSIS Sensitivity analysis [1] is the general term for quantitative study of how the inputs to a model influence the results of the model. Risk model involves uncertain inputs. The uncertainty of the inputs gets propagated to the output. In a decision making process it is desirable to have minimum of uncertainty in the conclusion. For this it becomes necessary to reduce the uncertainty of the inputs. However it is not always feasible to treat each input separately and reduce its uncertainty. In such situation sensitivity analysis can be done to identify the input which is most sensitive to the model. After identifying the most sensitive input, further investigation can be done to improve upon the estimate of the input and thereby reduce its uncertainty. If small changes in an input parameter result in relatively large changes in a model’s output, the model is said to be sensitive to that parameter. Sensitive analysis has many manifestations in probabilistic risk analysis and there are many disparate approaches based on various measures of influence and response. Monte Carlo analysis can be viewed as a kind of sensitivity analysis itself ([2], [3], [6]) in that it yields a distribution describing the variability about a point estimate. In sensitivity studies, many Monte Carlo simulations explore the possible impact on the assessment results by varying the inputs. The process of varying an input by replacing it with an input having reduced uncertainty is called pinching. The following strategies are usually followed for pinching in PBA assessments: (i) replace an input with a point value, (ii) replace an input with a precise distribution function, (iii) replace an input with a zero-variance interval. (iv) replace an input with an uncertain number with smaller uncertainty.