Prozessentwicklung

Strukturierung

Schritte	A	B	C
$0$	$100$	$100$	$100$
$1$	$\begin{array}{lcl} 120 & = & 0.8 \cdot 100 \\ & + & 0.1 \cdot 100 \\ & + & 0.3 \cdot 100 \end{array}$	$\begin{array}{lcl} 90 & = & 0.1 \cdot 100 \\ & + & 0.7 \cdot 100 \\ & + & 0.1 \cdot 100 \end{array}$	$\begin{array}{lcl} 90 & = & 0.1 \cdot 100 \\ & + & 0.2 \cdot 100 \\ & + & 0.6 \cdot 100 \end{array}$
$2$	$\begin{array}{lcl} 132 & = & 0.8 \cdot 120 \\ & + & 0.1 \cdot 90 \\ & + & 0.3 \cdot 90 \end{array}$	$\begin{array}{lcl} 84 & = & 0.1 \cdot 120 \\ & + & 0.7 \cdot 90 \\ & + & 0.1 \cdot 90 \end{array}$	$\begin{array}{lcl} 84 & = & 0.1 \cdot 120 \\ & + & 0.2 \cdot 90 \\ & + & 0.6 \cdot 90 \end{array}$
...	...	...	...

Schritte	Verteilungsvektor	Berechnung
$0$	$\vec{v}_0 = \begin{pmatrix} 100 \\ 100 \\ 100 \end{pmatrix}$
$1$	$\vec{v}_1 = \begin{pmatrix} 120 \\ 90 \\ 90 \end{pmatrix}$	$\vec{v}_1 = P \cdot \vec{v}_0 = \begin{pmatrix} 0.8 & 0.1 & 0.3 \\ 0.1 & 0.7 & 0.1 \\ 0.1 & 0.2 & 0.6 \end{pmatrix} \cdot \begin{pmatrix} 100 \\ 100 \\ 100 \end{pmatrix}$
$2$	$\vec{v}_2 = \begin{pmatrix} 132 \\ 84 \\ 84 \end{pmatrix}$	$\vec{v}_2 = P \cdot \vec{v}_1 = \begin{pmatrix} 0.8 & 0.1 & 0.3 \\ 0.1 & 0.7 & 0.1 \\ 0.1 & 0.2 & 0.6 \end{pmatrix} \cdot \begin{pmatrix} 120 \\ 90 \\ 90 \end{pmatrix}$
...	...	...
$n$	$\vec{v}_n = \cdots$	$\vec{v}_n = P \cdot \vec{v}_{n-1}$