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published: 23.02.2012 last modified:23.02.2012

Reduced Operaions



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Process operation, which is reduced to a comparable value can also lead to its borders.

Time moment corresponding to the complete transformation of input products of an agreed operation is defined as moment of operation’s physical completion (MOPC). MOPC is marked as tf on the diagrams. In turn, any process can be presented as a reduced vector operation (fig.1).

Временной ряд регистрации движения входных продуктов приведенной операции
re(t) - current value of a cumulative cost estimate of input products
Временной ряд регистрации движения целевого продукта приведенной операции
pe(t) - current value of a cumulative cost estimate of input products
Figure 1: The model, which shows the signals to the boundaries of technological operations

Consequently, it is important to determine the amplitudes of ES input and output signals.

Input product cost for the studied technological process at a certain moment of time is determined in the following way:


where re(t) - current value of a cumulative cost estimate of input products;
ts - the moment of process beginning;
pe(t) - current value of a cumulative cost estimate of input products;
tf - moment of operation’s physical completion.
RE and PE are the amplitudes of signals reflecting integral values of registered characteristics and, therefore, of input and output products in comparable values.

An impulse signal – RE is correlated with the moment of process beginning (ts) and provides re(t) function forming, and an impulse signal – PE is correlated with MOPC to form the pe(t) function.


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