The Analytic Hierarchy Process has found its way into various
decision areas. To perform decision analysis using AHP
includes four steps: setting up the decision hierarchy,
collectin input data, using a estimation method to estimate the
relative weights of decision elements, and arrive at a set of
ratings for the decision alternatives. It provides a more
systematic way to make a decision. In this paper, we intend to
include the random errors of the judgements of pairwise
comparison and the notion of randomness to strengthen AHP
methodology. We focus on a least squares estimation and a
best linear unbiased estimation of and compare statistical
properties between Saaty''s eigenvalue method vector of relative
weights, and least squares method. We release the constraint
that the input matrix must be a reciprocal one. And we take
all the elements of input matrix to measure the consistency of
input data. Furthermore, we construct the testing hypotheses
for consistency index to analysis the reliability of the order
of relative weights. Then, we apply these procedures in cases
to illustrate how one can go through it.