The Discrete-time Modeling, Analysis And Application For The Instantaneous Availability Of The Systems Under General Probability Distribution

Equipment Operational Readiness and continuity of mission are important elements of equipment combat power. Availability of equipment is an important parameter of well describing equipment Operational Readiness and continuity of mission. In practical using, equipment availability parameters can be generally divided into steady-state availability parameters and instantaneous availability parameters. For a long time, the research and application of steady-state availability has brought wide attention. However, with equipment's function being more and more complicated, the fault-mechanism and maintaining-rules become more and more difficult to be understood and controlled. The equipment availability presents a series of fluctuation phenomenon in the using process. Obviously, these phenomena can be neither explained nor further studied via the traditional methodology of steady-state availability.Based on a careful analysis and discussions of the current existing equipment instantaneous availability model, this dissertation focuses on the problems of the equipment instantaneous availability modeling and its specific application on the instantaneous availability analysis and designs. The main works are as follows.First, in order to study the issue of instantaneous availability in details, the existing continuous-time model of availability and its approximate solution are discussed under the general distribution. The studies reveal that the computational accuracy of the discretelized solving methodology is satisfactory, but the expression as well as the computation of the approximate solution is usually very complicated and hence not very convenient for the further applications. Especially, the discrete-time characteristic of the practical maintenance is not very applicable for the descriptions of continuous-time availability models either.Then, in order to overcome the shortcomings of the existing continuous-time models of the instantaneous availability, a kind of new discrete-time instantaneous availability model is proposed for one-unit repairable systems, two-unit series and parallel-connected repairable systems with repair-delays, and the repairable system with preventive maintenance.Moreover, the relationship between the continual-time and the discrete-time of instantaneous availability model is investigated. The numerical solutions of the proposed discrete-time models are compared with exactly analytic solutions of the continual-time models under the exponential distribution. The comparison shows that the discrete-time model has the advantages of satisfactory computational-precision and less time-consuming. Under suitable sampling-rate, the proposed discrete-time models can substitute for the continual-time model.Finally, based on the proposed discrete-time instantaneous availability model, two types of optimization design problems, namely, the smallest availability fluctuation problem and the track problem, are well formulated. Some numerical analysis is carried out on the discrete-time one-unit repairable system and the discrete-time one-unit repairable system with repair delays using the Particle Swarm Optimization Algorithm.Studies reveal that the fluctuation phenomenon of instantaneous availability can be refrained by matching-design the fault-rate, maintaining rate, and delays-repair rate appropriately in a pre-specific extent.