  A statistical approach based on the interval analysis (IA) is proposed for
the analysis of the effects, on the radiation patterns radiated by phased
arrays, of random errors and tolerances in the amplitudes and phases of the
array-elements excitations. Starting from the efficient, reliable, and
inclusive computation of the bounds of the complex-valued interval array
pattern function by means of IA, an analytic method is presented to yield
closed-form expressions for the probability of occurrence of a user-chosen
value of the power pattern or of its features within the corresponding
IA-derived bounds. A set of numerical examples is reported and discussed to
assess the reliability of the proposed probabilistic interval analysis (PIA)
method with the results from Monte Carlo simulations as well as to point out
its effectiveness and potentialities/advantages/efficiency in real applications
of great industrial interest.
