Reliability optimization of series-parallel systems with a choice of redundancy strategies using a genetic algorithm

Abstract

This paper proposes a genetic algorithm (GA) for a redundancy allocation problem for the series-parallel system when the redundancy strategy can be chosen for individual subsystems. Majority of the solution methods for the general redundancy allocation problems assume that the redundancy strategy for each subsystem is predetermined and fixed. In general, active redundancy has received more attention in the past. However, in practice both active and cold-standby redundancies may be used within a particular system design and the choice of the redundancy strategy becomes an additional decision variable. Thus, the problem is to select the best redundancy strategy, component, and redundancy level for each subsystem in order to maximize the system reliability under system-level constraints. This belongs to the NP-hard class of problems. Due to its complexity, it is so difficult to optimally solve such a problem by using traditional optimization tools. It is demonstrated in this paper that GA is an efficient method for solving this type of problems. Finally, computational results for a typical scenario are presented and the robustness of the proposed algorithm is discussed.

Introduction

The primary goal of reliability engineering is to improve the reliability system. In the initial design activity, the redundancy allocation is a direct way of enhancing system reliability. The redundancy allocation problem involves the simultaneous selection of components and a system-level design configuration, which can collectively meet all design constraints in order to optimize some objective functions such as system cost and/or reliability [1]. This reliability design problem has generally been formulated by considering active redundancy. To deal with these problems, a large number of models and solution methods have been proposed such as dynamic programming, Lagrangean multiplier [2], heuristic approach [3], integer programming [4], and genetic algorithms (GAs) [5]. Comprehensive overviews of these methods have been addressed by Kuo et al. [6] and Gen et al. [7]. Furthermore, the redundancy allocation problem is considered for various system structures such as series, parallel, network, parallel-series [8], k-out-of-n [9] and the like. The series-parallel system, as depicted in Fig. 1, is a common system structure that is used in most system designs. Thus, the series-parallel redundancy allocation problem is considered in this paper.

The above-mentioned solution methodologies for series-parallel systems are not applicable when the system design involves active and cold-standby redundancies. Coit [9] presented a new problem formulation and solution method to determine the optimal system design configuration when a system design includes multiple subsystems that are designed with either active or cold-standby redundancy. This solution method assumes that the redundancy strategy (active or cold-standby) for each subsystem is predetermined. However, the choice of these two redundancy strategies for each subsystem is much more realistic and it provides a better tool for the designers. Coit [10] also presented an optimal solution to redundancy allocation problems when there are some subsystems using active redundancy, cold-standby redundancy, or selecting the best redundancy strategy. This becomes an additional decision variable in redundancy allocation problems. Coit [10] solved this problem by first formulating it and then applying a zero-one integer programming method.

Chern [11] showed that even a simple redundancy allocation problem in series systems with linear constraints is NP-hard. This has prompted recent researchers to develop metaheuristic methods to achieve approximate solutions of acceptable quality in a reasonable computational time. Metaheuristic methods can be used to solve complex discrete optimization problems. These methods provide more flexibility and require fewer assumptions on the objective function and the associated constraints. A GA is one of the metaheuristic methods trying to imitate the biological phenomenon of evolutionary production through the parent–children relationship [12]. Recently, GAs have been designed to solve a variety of reliability optimization problems. Coit et al. [1] successfully applied a GA for redundancy allocation problems.

The structure of this paper is organized as follows. 2 Redundancy strategies, 3 Problem formulation present a review on the redundancy strategies and the problem formulation, respectively. In Section 4, a GA is proposed for solving the redundancy allocation problem when either active or cold-standby redundancy can be selected for individual subsystems. Section 5 considers a numerical example to demonstrate the efficiency of the proposed methodology through computational results. Finally, Section 6 presents conclusion.