A new approach to solving problems of multi‐state system reliability optimization

Abstract

SUMMARYUsually engineers try to achieve the required reliability level with minimal cost. The problem of total investment cost minimization, subject to reliability constraints, is well known as the reliability optimization problem. When applied to multi-state systems (MSS), the system has many performance levels, and reliability is considered as a measure of the ability of the system to meet the demand (required performance). In this case, the outage effect will be essentially different for units with different performance rate. Therefore, the performance of system components, as well as the demand, should be taken into account. In this paper, we present a technique for solving a family of MSS reliability optimization problems, such as structure optimization, optimal expansion, maintenance optimization and optimal multistage modernization. This technique combines a universal generating function (UGF) method used for fast reliability estimation of MSS and a genetic algorithm (GA) used as an optimization engine. The UGF method provides the ability to estimate relatively quickly different MSS reliability indices for series-parallel and bridge structures. It can be applied to MSS with different physical nature of system performance measure. The GA is a robust, universal optimization tool that uses only estimates of solution quality to determine the direction of search.

Optimal Allocation of Reliability in Series Parallel Production System

“…In this paper, an MSS reliability theory will be used, where the binary state system theory is extending to the multi-state case. As is addresses in recent review of the literature for example in (Ushakov, Levitin and Lisnianski, 2002) or (Levitin and Lisnianski, 2001). Generally, the methods of MSS reliability assessment are based on four different approaches:…”

“…It was proven to be very effective for high dimension combinatorial problems: see e.g. (Ushakov, 2002), (Levitin, 2001). The universal moment generating function is an extension of the ordinary moment generating function (UGF) (Ross, 1993).…”

Reliability Analysis of Wind Turbines Considering Constraints and Legislation

“…Metaheuristics that are used in both the articles compared may find an approximation of the local or global minimum topology, but rarely the exact solution. For information, our UGF model has been tested and compared with ones already conducted [41].…”

“…What make more complicated to deal with these constraints is the multi-state system (MSS) that represent the wind farm. Even if the MSS reliability measures were intensively studied in [18]- [20], only few articles were found that deal with this reliability optimization including environment effects [21]. Thus, studying the topology optimization of wind farm under constraints of wind, performance and costs turn to be a good research gap.…”

Multi-objective availability-redundancy allocation problem for a system with repairable and non-repairable components

“…In most cases, the problem of availability allocation and optimization can be defined as a multi-objective optimization problem, which aims to maximize system availability and minimize tits cost (Elegbede & Adjallah, 2003). Levitin and Lisnianski (2001) introduced a model in which the cost of designing the system is fixed and its purpose is to optimize system availability. Also, Zio and Bazzo (2011) presented an analysis on level diagrams of Pareto front for the redundancy allocation problem.…”