Abstract: This paper proposes the concept of weak prognosability.For fault detection,prognosis can reduce the loss caused by faults to the system more than diagnosis.However,even if most fault strings are prognosable,as long as one fault string is unprognosable and can only be diagnosed,the whole system is unprognosable and can only be handled by diagnosis,which is unfavorable to most fault strings.The concept of weak prognosability can avoid this situation.Weak prognosability is the prediction of whether the system will be in a fault state in the future.Compared with prognosability,weak prognosability does not require all fault event strings to be prognosable.Weak prognosability can alarm the prognosable fault strings before the fault occurs,and it can also alarm the unprognosable but diagnosable fault strings after the fault occurs.A verifier is constructed to test the weak prognosability of the system,a polynomial algorithm of weak prognosability of the system is given based on the verifier,and the sufficient and necessary conditions of weak prognosability are also given.

Key words: Discrete event system, Fault prognosis, Weak prognosability, Polynomial complexity, Automata