Reliability Analysis Of A Man-Machine System With Critical And Non-Critical

Since the birth of reliability theory, many scholars have been begining to study the reliability theory,resulting in the gradual improvement of the reliability theory, and research areas is constantly spreading.Whether the study of material fatigue life,or military secu-rity,equipment replacement,the field of aerospace, medical, machine maintenance and other aspects of research, reliability theory are indispensable theoretical basis.This paper presents the man-machine mathematical model of repairable system with two different human error.To begin with,existence and uniqueness of the non-negative solution of the system is discussed in Banach Space.Followed by analyzing spectrum location of the system operators,and we prove that only0is the simple eigenvalues with its algebraic multiplicity is spectral point,thus the asymptotic stability of the system is proved.Then the system with quasi-compactness is proved,thus we have came to the exponential stability of the system. In addition,in general we know that the instantaneous solution of the system is not easy solutions,and sometimes is unable to solve the instantaneous solution. Therefore, the instantaneous solution of the monotone case, we can use the index matrix and combined with the spectral decomposition method to discuss in the instantaneous reliability of two different systems, by comparison of instantaneous reliability of two different systems with each state,and then the conclusion has been drawn.that is,in the specific case,when (?)t>0and the failure rateλ0tends to infmity,by the comparison of instantaneous reliability p1(t) of the two models system.We get The next we infer that the instantaneous stability of the system approach to the instan-taneous stability of the weak solution of the system,so we obtain that the strong solution of the system model approaches to weak solution of the system.In conclusion,we are in the form of the cha,rt to show that the steady-state availability of two systems relative error close to zero,as the failure rate λ0tends to infinity. Above by comparison of the steady state availability, we get the system in terms of reliability, work efficiency and economic benefits have increased. Therefore the reliability of the research system is necessary.