System Reliability Analysis Based On Possibility Theory And Lattice Theory

Reliability engineering has aroused intensive attention in our country for the pasthalf century. Reliability theory has been continuously developed and increasinglyapplied to a variety of industrial regions. It was first applied in electronic productsduring the early seventies; thereafter, reliability research was utilized in various fieldssuch as aeronautical/space technologies, nuclear energy, and communication systems.As for the complex structure in practical engineering, natural language is widely used toconvey the fuzzy information. It is observed that the traditional probabilistic method isdifficult to handle the fuzzy characteristic within natural language. Therefore, there is anurgent need to develop possibility theory to transform the natural language propositionand carry out the quantitative analysis in reliability theory.Currently, conventional binary reliability theory is based on the assumption thatsystem state is limited by only two possible states: perfectly function and completelyfail to function, which is an oversimplification of the practical situations. Based on this,experts and scholars introduced and developed the multi-state reliability theory.Considering the fact that system states are of incomparable characteristic in actual life,the original assumption of system and component state set being totally ordered set isdifficult to completely describe the actual system or component states. As a furtherdiscussion, lattice theory is developed in system reliability research, which describes thepartial order within system or component state space.This dissertation aims to address key challenges and critical issues within thedevelopment of system reliability theory, and with a special emphasis on twofundamental aspects: epistemic uncertainty and system state’s incomparablecharactristic. Taking advantage of possibility theory and lattice theory, the primaryresearch contributions and innovative achievements are summarized as follows.1. Extendence of system possibilistic reliability theory based on the concept ofconvex sublattice. The definition of convex sublattice is extended from the subset’sconvex structure. Supposing that system state set is a complete lattice, Doctor Cappelleand Kerre introduced the equivalence class of structure function on the basis of congruence relation. Based on their work, this dissertation introduces the concept ofconvex lattice to the process of system possibilistic reliability analysis. As for thecomplete lattice composed of all the structure functions, it can be concluded that theupper (lower) bound set of structure function’s equivalence class are the convexsublattice. Thus, the supremum and infimum of the upper (lower) bound set of structurefunction’s equivalence class can be figured out. Different structure function stands fordifferent system structure. It is proved that the scope of structure function can benarrowed through the observation set. As a result, the related definitions and propertiesturn out to be meaningful both in theoretical development and practical application.Meanwhile, the supremum and infimum of the upper (lower) bound set of structurefunction’s equivalence class makes the comparasion of structure functions becomingreality. Therefore, the goal of searching for better system structures is achieved.2. Systematic investigation of possibilistic reliability function analysis formulti-state systems. It is difficult to perform the system possibilistic reliability analysissince it is difficult to obtain the system state possibility distribution. In order toovercome this difficulty, state corresponding Most Possible Residual Lifetime (shortedas MPRL) is introduced to represent the internal functional relationship between systemstate and residual lifetime. System state corresponding Most Possible Residual Lifetime(MPRL) is defined as the system’s most possible remaining lifetime under the state,which bridges the gap between system state possibility distribution and system lifetimepossibility distribution. Moreover, introducing the variable of investigated momentwhich links the system state and corresponding most possible residual lifetime,possibilistic reliability function of multi-state system is redefined. As a result, systempossibilistic reliability analysis can be realized by system lifetime possibilitydistribution, while avoids the adoption of the inconvenient state possibility distribution.3. Development of system reliability theory on the repairable systems with omittedor delayed failure effects. Within the practical problems in industrial engineering, thefailure effects sometimes can be omitted or delayed if it has neglibile effect on thesystem. Taking a two-unit parallel system on as the research theme, the modelassumption of the new system with repair time omission is given based on the originalsystem. New system’s reliability indices can be presented on the basis of probabilitytheory and system reliability theory. Afterwards, single-unit repairable systems with omitted or delayed failure effects are analyzed in view of possibility theory. Bydifferentiating between the original single-unit repairable system and the newsingle-unit repairable system with omitted or delayed failure effects, new systempossibilistic reliability is analyzed and instantaneous possibilistic availability isobtained.4. System reliability analysis for multi-state systems whose state set is modeled bycomplete lattice. Based on the existence of the incomparable system or component state,complete lattice on the partial order relation is adopted to substitute the totally orderedset to present the multi-state system state set. Supposing that system or component statespace is characterized by complete lattice, typical systems such as a single-unit system,a series system and a parallel system are discussed based on probability theory andpossibility theory, respectively.