استفاده از روش نمونه گیری مکعب لاتین درختی به منظور برآورد واریانس نمونه گیری در عدم قطعیت و نتایج تجزیه و تحلیل حساسیت برای دفع زمین شناختی زباله های رادیو اکتیو

The 2008 performance assessment (PA) for the proposed repository for high-level radioactive waste at Yucca Mountain (YM), Nevada, used a Latin hypercube sample (LHS) of size 300 in the propagation of the epistemic uncertainty present in 392 analysis input variables. To assess the adequacy of this sample size, the 2008 YM PA was repeated with three independently generated (i.e., replicated) LHSs of size 300 from the indicated 392 input variables and their associated distributions. Comparison of the uncertainty and sensitivity analysis results obtained with the three replicated LHSs showed that the three samples lead to similar results and that the use of any one of three samples would have produced the same assessment of the effects and implications of epistemic uncertainty. Uncertainty and sensitivity analysis results obtained with the three LHSs were compared by (i) simple visual inspection, (ii) use of the t-distribution to provide a formal representation of sample-to-sample variability in the determination of expected values over epistemic uncertainty and other distributional quantities, and (iii) use of the top down coefficient of concordance to determine agreement with respect to the importance of individual variables indicated in sensitivity analyses performed with the replicated samples. The presented analyses established that an LHS of size 300 was adequate for the propagation and analysis of the effects and implications of epistemic uncertainty in the 2008 YM PA.

Latin hypercube sampling is a very effective and popular procedure for the propagation of epistemic uncertainty in analyses of complex systems [1], [2] and [3]. The effectiveness and resultant popularity of Latin hypercube sampling derives from the fact that a relatively small Latin hypercube sample (LHS) can be used in the generation of a mapping between uncertain analysis inputs and corresponding uncertain analysis results that can then be successfully explored with a variety of uncertainty and sensitivity analysis procedures [4]. Analyses of complex systems typically involve large and computationally demanding models. As a consequence, it is necessary to use an efficient sampling procedure such as Latin hypercube sampling in the propagation of epistemic uncertainty as the number of model evaluations that can be performed is limited by computational cost. For example, the U.S. Nuclear Regulatory Commission's (NRC's) reassessment of risk from commercial nuclear power plants used LHSs of size 200 and 250 from approximately 150 to 200 epistemically uncertain analysis inputs in probabilistic risk assessments (PRAs) for five nuclear power stations [5], [6], [7], [8], [9], [10] and [11], and the U.S. Department of Energy's (DOE's) performance assessment (PA) for the Waste Isolation Pilot Plant (WIPP) carried out in support of a successful Compliance Certification Application [12] and [13] to the U.S. Environmental Protection Agency (EPA) used an LHS of size 100 from 57 epistemically uncertain analysis inputs [14]. The indicated reactor PRAs are often referred to as the NUREG-1150 PRAs in consistency with the associated NRC report [11]. The potential effectiveness, and hence appropriateness, of the use of the indicated small sample sizes in complex and important analyses is open to question and needs to be established. In response to this need, a replicated sampling procedure has been proposed to establish the adequacy of the use of small LHSs in the analysis of complex systems [15]. This procedure has been used to establish the adequacy of the LHS sizes in the NUREG-1150 PRAs [16], the WIPP PA [13] and [17], and an analysis with the MACCS reactor accident consequence model [18]. A recently completed large analysis that used replicated Latin hypercube sampling to assess the stability of uncertainty and sensitivity analysis results obtained with a relatively small LHS is the 2008 PA for the proposed Yucca Mountain (YM) repository for high-level radioactive waste [19]. Specifically, this analysis used an LHS of size 300 to propagate 392 epistemically uncertain variables through a complex analysis involving a large number of linked models. The purpose of this presentation is to describe the use of replicated Latin hypercube sampling in the 2008 YM PA. The following topics are considered: (i) definition and properties of replicated sampling (Section 2), (ii) stability of uncertainty analysis results (Section 3), and (iii) stability of sensitivity analysis results (4 and 5). The presentation then ends with a summary discussion (Section 6). This presentation is based on a talk [20] given at the 2010 Sensitivity Analysis of Model Output (SAMO) conference held in Milan, Italy, and is part of a special issue of Reliability Engineering & System Safety containing papers presented at this conference. A companion paper in this special issue contains a description of the 2008 YM PA and provides an adequate level of background for this presentation on replicated sampling in the 2008 YM PA [21]. More detailed information on the 2008 YM PA is available in Ref. [19] and in the large number of model-specific reports cited in this reference. A less detailed overview of the 2008 YM PA is available in a sequence of conference papers [22], [23], [24], [25], [26], [27] and [28]. A special issue of Reliability Engineering & System Safety on the 2008 YM PA is also currently in preparation.