The paper deals with the diagnosis of continuous-variable systems whose sta
te can be measured only by means of a quantizer Hence, the on-line informat
ion used in the diagnosis is given by the sequences of input and output eve
nts. The diagnostic algorithm uses a representation of the quantized system
by means of a semi-Markov process, which provides a timed description of t
he event sequences generated by the quantized system. The paper describes h
ow the probability density function of the semi-Markov process can be deter
mined for a given quantized system. The diagnostic algorithm can be applied
on-line, because it determines the fault probabilities recursively for the
sequence of input and output events. The result is illustrated by a numeri
cal example which concerns a part of a batch process.