Reliability Modeling and Resource Pooling of Complex Systems


Student thesis: Doctoral Thesis

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Awarding Institution
Award date20 Aug 2018


With the growth of manufacturing technology, industrial products and systems are be- coming more complex to satisfy the high-quality standards. The complex systems can have multiple failure mechanisms, heterogenous operating components, or intricate system structures. Motivated by this, a considerable amount of work has been devoted to reliability modeling and optimization of complex systems.

First, from the prospective of component level, a new reliability model by considering the damage self-healing phenomenon is developed. Systems experiencing multiple dependent competing failure processes (MDCFP) have attracted much attention in the recent years. Like the biological systems, which can heal after being wounded; damage self-healing exists in many systems and products due to the intrinsic resistance to abrupt damage. For each random shock, we propose healing time and healing level concept to describe the self-healing process. The system reliability efficiently evaluated by using simulation method. It is shown that the proposed model is general model that can be transformed into many classical degradation and shock models in different parameter settings.

Second, a new Weibull inter-arrival shock process is proposed for modeling the competing risk process. The Weibull inter-arrival shock process generalized the Pois son shock process and can deal with the cases when the shock count data are over- dispersion or under-dispersion. On the other hand, the dependency between the soft failure process and hard failure process is emphasized by assuming the linear de- pendent damage size. In three different hard failure models, analytic forms of the reliability functions are derived by using the polynomial expansion. The maintenance optimization for the developed model is discussed under different shock failure mechanisms.

Next, from the prospective of system level, we consider a series system with a performance sharing group of limited size, i.e., the number of elements that can be connected into the performance sharing group is limited. It is assumed that the elements connected into the performance sharing group can change dynamically when the state of the system changes to minimize the possible performance deficiency of the system. A reliability evaluation algorithm is proposed for the suggested system and the optimal connection strategy is discussed. We also present a study of systems consisting of multi-state units connected as two performance sharing groups, and the suggested methodology can be adapted for the case of three or more performance sharing groups. An algorithm based on the universal generating function technique is proposed to evaluate the system reliability and the expected system performance deficiency.

Finally, the sharing mechanism also exists in various service systems and the allocation of profit/cost is a key issue lied in. Motivated by this, we study resource sharing whereby multiple independent service providers collaborate by pooling their resources into a single service facility and deploying an optimal scheduling policy for their customers collectively by accounting for their individual waiting costs and service level requirements. We model the pooled systems as M/M/c queueing systems with heterogeneous waiting costs subject to service level constraints. The optimal scheduling policy for such a system is a (mixed) priority policy. We investigate cost allocation rules to the pooled systems by applying concepts from cooperative game theory. We consider both the case with a fixed number of servers and the case with endogenous capacity optimization. To empower our analysis, we show that a cooperative game with polymatroid optimization can be analyzed via simple auxiliary games. By exploiting the analytical properties of the continuous extension of the total virtual workload and multiclass queueing systems with polymatroidal structures, we provide sufficient conditions for the games to possess a core allocation.