A semigroup S with a sub-band B is called a good B-quasi-Ehresmann semigroup if it is a Bsemiabundant semigroup satisfying the congruence condition such that B((ab)+)abB((ab)*)aB(a*)B(b+)b for all a,b ∈S.We show that every good B-quasi-Ehresmann semigroup has a global representation and a standard representation.As a special case,the structure of good quasi-adequate semigroups is described.
Reliability model of a mechanical product system will be newly reconstructed and maintenance cost will increase because failed parts can be replaced with new components during service,which should be accounted for in system design. In this paper,a reliability model and reliability-based design optimization methodology for maintenance are presented. First,based on the time-to-failure density function of the part of the system,the age distributions of all parts of the system during service are investigated,a reliability model of the mechanical system for maintenance is developed. Then,reliability simulations of the systems with Weibull probability density functions are performed,the system minimum reliability and steady reliability for maintenance are defined based on reliability simulation during the life cycle of the system. Thirdly,a maintenance cost model is developed based on replacement rates of the parts,a reliability-based design optimization model for maintenance is presented,in which total life cycle cost is considered as design objective and system reliability as design constrain. Finally,the reliability-based design optimization methodology for maintenance is used to design of a link ring for the chain conveyor,which shows that optimal design with the lowest maintenance cost can be obtained,and minimum reliability and steady reliability of the system can satisfy requirement of system reliability during service of the chain conveyor.
