Relative predictability of failure event occurrences and its opacity-based test algorithm

In this paper, the problem of relative predictability of failure event occurrences is investigated. The notion of relative predictability is proposed for logical automata and the concept of predictable rate is introduced to characterise the predictability property of a discrete-event system, which takes values in the interval [0, 1]. Intuitively, a discrete-event system being relatively predictable means that there exist some failure events which can be predicted from the observations of the system. The relationship between relative predictability and predictability introduced by Sahika Genc et al. analysed and the analysis shows that relative predictability is weaker than predictability for discrete-event systems. Furthermore, a necessary and sufficient condition for relative predictability is presented. In particular, an opacity-based algorithm is developed to test the relative predictability, which is polynomial in the number of states of the system. Also, some examples are provided to illustrate the presented results.