Modeling And Reliability Analysis Of State Aggregated Systems Driven By Demands

Multi-state systems are a type of important systems in the reliability theory, and are widely used in manufacture, production, water distribution, power generation, oil and natural gas and so on. The state numbers of multi-state systems are very huge, and the output power (or performance) is different when systems are in a state of different. Markov repairable systems are a special of multi-state systems. In the past study, the state space of the Markov repairable system is partitioned as working states and failure states, i.e., acceptable states and unacceptable states. In fact, whether the state of the system can be accepted or unaccepted depends on the relationship of the Markov repairable system performance and the demand performance. In real life, the demand of custermers (users) is varied. Therefore, it is important to carry on demand management. Developing state aggregated system models driven by demand have theoretical significance and application value. In this dissertation, state aggregated system models driven by demand are built based on the system output power (or performance) and the demand performance. Reliabiliy analysis for these systems are considered by employing ion-channel modeling theory, aggregated stochastics process and Krnonecker operator. The manin research parts of this dissertation are follows.Firstly, Markov supply state aggregated system models driven by deterministic demand are built. Several new reliability indexes are proposed, i.e., multi-point availability, multi-interval availability and mixed multi-point-interval availability. The calculation formulas are presented for these new reliability indexes. In these systems, the demand patterns are deterministic and the supply patterns are a Markov stochastic process.Secondly, Markov supply state aggregated system models driven by deterministic demand in random environments are built. Several new reliability indexes under environments condition are proposed, i.e., multi-point availability, multi-interval availability and mixed multi-point-interval availability. The calculation formulas are presented for these new reliability indexes. In these systems, systems operate in random environments. Some states of these systems are changeable, i.e., some states of these systems are working states in some environments, however, these states may be failure states in other environments. Some environments are fatal to these systems, i.e., all stats of these systems under these environments are failure states.Thirdly, Markov supply state aggregated system models with multi-working levels driven by deterministic demand are built. Several new reliability indexes are proposed by considering out powers of the system, i.e., multi-point availability, multi-interval availability and mixed multi-point-interval availability. The calculation formulas are presented for these new reliability indexes. In these systems, the demand patterns are deterministic, and custermers have different levels of demand in different times. The supply states are lumped together according to their membership as a common working level. The whole supply states are can be partitioned into several working levels.Fourthly, Markov supply state aggregated system models with multi-working levels driven by Markov demand are built. Several new reliability indexes are proposed, i.e., the probabilities that the custemor requirements are met at a certain time interval. The calculation formulas are presented for these new reliability indexes. In these systems, both of the supply patterns and the demand patterns are stochastic. We are interested in the probability that demands of custermers are satisfied at a certain time interval.Fifthly, Markov supply state aggregated system models with multi-working levels driven by Markov demand with multi-working levels are built. Several new reliability indexes are proposed, i.e., the probabilities that the custemor specific requirements are met by corresponding levels of supply at a certain time interval. The calculation formulas are presented for these new reliability indexes. In these systems, both of the supply patterns and the demand patterns have multi-working levels. Custermers have different levels of demand in different times, and the levels of supply are different in different times. The supply states and demand states are lumped together according to their membership as a common working level, respectively. The whole supply states and demand states are can be partitioned into several working levels, respectively.Reliability measures of systems developed in the dissertation are analysised. Several reliability indexes correspongding to systems developed in the dissertation are obtained. Numerical examples are employed to verify the results. The Markov supply state aggregated system models driven by deterministic demand and the Markov supply state aggregated system models with multi-working levels driven by deterministic demand are used to analysis the reliability measures of a micro-computer system, respectively. The research of this dissertation has important theoretical values and practical significance. It can push the development of state aggregated system models driven by demand and aggregated stochastic processes. It can also provide theory reference for the maintenance optimization and planning, reliability evaluation, management of multi-state systems.