ABSTRACT
To determine the state of the system, the values of the features compared with standard requirements need to be known (Fiok et al. 1998). The values of features are obtained by means of system monitoring. For the WSS, the features are water quality and quantity, which are understood as a supply. As a rule, monitoring is managed by a system operator who also qualifies the measurement data. It is assumed that: R = P(Y = 1) – system dependability qualified by an operator Q = P(Y = 0) – system unreliability qualified by an operator A measure of the first type of error is the probability of an event:
A measure of the second type of error is the probability of an event:
Let D be an experience with the probable results C1, C2,… Cn, which is executed with the probabilities P1, P2… Pn, then the information received as a result of experience D is a random variable that takes values –log Pi, i = 1,2…n on a set Ci. An expected value of this information is called the experience entropy H(D) and is:
In some sense, the experience entropy is a measure of its indefiniteness and it can be used to control the states of the system. The more equal the probabilities of states, the bigger the entropy; the higher the difference in the probabilities of states, the lower the entropy (Bishop 2006). If the given event occurs with a probability of 1, then, as results from a simple substitution, the entropy is 0, because it is known in advance what will happen – uncertainty does not exist. The entropy (H), which is a measure of indefiniteness of system states, is calculated from the formula:
It should be noticed that if Pi = 1, then H = 0, and if the probabilities Pi are equal and are 1/n, then H = ln n, obtaining the maximal value.
