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236 Biofuels for a More Sustainable Future

quasi-Monte Carlo sampling, pseudo-Monte Carlo sampling, Hammersley
sequence sampling, and Latin hypercube sampling (Giunta et al., 2003).
When applying DOE to the computational results of models that result
from LCA or LCC, the input parameters are considered to be the indepen-
dent variable of the experiment and combination of levels in the input
parameters in the model are considered as experimental “treatments.”
The purpose of the analysis is the attribution of uncertainty of final results
to various sources of error in the inputs. Typically, the input parameters cho-
sen to be used as the independent variables in the DOE are those whose esti-
mates the model creator expects to be most unpredictable or the least
reliable.
Another advantage of DOE for the analysis of models is that it allows the
quantification of factor independence with a rigorous statistical framework.
Specifically, the Latin hypercube method estimates linear and quadratic
effects and bilinear interactions (Ye, 1998) to obtain low-order polynomial
models. These polynomial models serve as approximations of the underly-
ing, more complex model and are easier to understand on an intuitive level.
On the other hand, while the traditional local or one-at-a-time sensitivity
analysis is easier to implement, the polynomial models provide more infor-
mation including interaction effects and confidence intervals for the polyno-
mial coefficients.
In the next section, we show an example wherein a simple model for the
financial life-cycle cost of biodiesel in Vietnam and analyze the sensitivity of
the life-cycle cost to selected parameters. This is a more detailed exposition
of results previously published in Khang et al. (2017, 2018).

2 Example of sensitivity analysis of biodiesel via DOE
2.1 Financial LCC of biodiesel
Ong et al. (2012) proposed a simple model for estimating the financial life-
cycle cost of a palm oil biodiesel. It is easily translated to other feedstocks as
will be done here. For a project life of n years, the life-cycle cost, here taken
as the present value of the project, can be defined as
LCC ¼ CC + OC + MC + FC SV BP (8.11)

where
CC¼capital cost
P n OR PC
OC¼operating cost (US$) ¼ i:
l + rÞ
i¼l ð