Narrow Results

The paper presents a heuristic for series-parallel system, exhibiting multi-state behavior, with the objective to minimize the cost in order to provide a desired level of reliability. System reliability is defined as the ability to satisfy consumers demand and is presented as a piecewise cumulative load curve. The components are binary and chosen from the list of products available in the market, and are being characterized by their feeding capacity, reliability and cost. The solution approach makes use of heterogeneous collection of components to provide redundancy in a subsystem. The algorithm has been applied to power systems from the literature for various levels of reliability requirement. The heuristic offers a straightforward analysis and efficiency over genetic algorithm (GA) existing in the literature. Keeping in view the computational efficiency and the observed solution quality the proposed heuristic is appealing. As such, the heuristic developed is attractive and can be easily and efficiently applied to numerous real life systems.

This paper addresses the redundancy allocation problem of multi-state series-parallel reliability structures where each subsystem can consist of maximum two types of redundant components. The objective is to minimize the total investment cost of system design satisfying system reliability constraint and the consumer load demand. The demand distribution is presented as a piecewise cumulative load curve. The configuration uses the binary components from a list of available products to provide redundancy so as to increase system reliability. The components are characterized by their feeding capacity, reliability and cost. A system that consists of elements with different reliability and productivity parameters has the capacity strongly dependent upon the selection of components constituting its structure. An ant colony optimization algorithm has been presented to analyze the problem and suggest an optimal system structure. The solution approach consists of a series of simple steps as used in early ant colony optimization algorithms dealing with other optimization problems and still proves efficient over the prevalent methods with regard to solutions obtained/computation time. Three multi-state system design problems have been solved for illustration.

The multi-state consecutive linear (circular) $k$-out-of-$r$-from-$n:F$ system consists of $n$ linear (circular) ordered multi-state components. Both the system and its components can have $m$ different states: from complete failure (zero state) up to perfect functioning (($m-$1) state). In this paper we suggest, for the first time, exact reliability for these models. The system is at state below $j$ if and only if at least $k_j$ components out of any $r$ consecutive are in state below $j$$(k_1\le k_2\le \cdots \le k_{m-1})$. Recent efforts in these branches have focused on simple situations or approximation bands for their reliability in two-state or multi-state models but closed form and exact amount not gained. In the continuation, there are the matlab programs of linear (circular) reliability system and $j$ state probability for $k_j$ in system. In the following, we applied comparative and numerical results and calculated the exact reliability of this strategic systems. Finally, we calculated the exact reliability for two real-world practical examples.

In this study, we focus on the reliability evaluation of the linear consecutive-$k$-out-of-$n$:G system, where the system is working if and only if at least $k$ consecutive components work. The multiple state of the system is considered including not only the working and failure state, but also the intermediate state approaching failure, and the reliability evaluation is discussed including the system failure probability, the expected number of failed components and the expected time to the considered intermediate state. We also apply these reliability results to the maintenance problems, and discussed the condition-based maintenance for the system which is based on the state of the system, and give the results of the optimal maintenance interval which minimizes the expected cost rate.