On-line quality control during production calls for monitoring produced items according to some prescribed strategy. It is reasonable to assume the existence of system internal non-observable variables so that the carried out monitoring is only partially reliable. In this note, under the setting of a Hidden Markov Model (HMM) and assuming that the evolution of the internal state changes are governed by a two-state Markov chain, we derive estimates for false-alarm and non-detection malfunctioning probabilities. Kernel density methods are used to approximate the stable regime density and the stationary probabilities. As a side result, alternative monitoring strategies are proposed.