ABSTRACT
Look at Figure 7.15. We have two states: which means repair and which means work and this state consists of two sub-states. The principle of the construction of this chain relies on the production of the following matrix of probabilities:
From to
From to
From to
From to
P P
P P
that yields to10:
1 0
0 P23 0
(7.22)
where the fact that state consists of two sub-states is taken into account. Now, we are going to find the ergodic probability distribution-usually denoted by Π-for this
Markov chain. The following matrix equation holds:
Π = Π (7.23)
The probability distribution Π consists of three elements-probabilities-because we have three states of the process:
Π = (Π 1 Π
Changing equation 7.23 into the coordinate form we have:
−
− =
− =
⎧ ⎨⎪ ⎩⎪
Π Π Π Π Π Π Π
p
0 0
(7.24)
Unfortunately, this set of equations is indeterminable. Therefore, it is necessary to reject one equation and replace it with the equation closing all probabilities to unity (see Chapter 7.1).
