Reliability Allocation Problem in Series-Parallel Systems: Ant Colony Optimization

Introduction

Quality and safety management of production tools is a great challenge for industries. This leads them to develop cost management policies adapted to the encountered problems. For example, let consider the case of a hospital which must change its electrical power system. It is obvious that, in case of electricity breakdown, it must have one or two other reliable electricity systems. Its aim is to have electrical power systems (in redundancy, i.e., in parallel) which are reliable and not expensive. The hospital must study the reliability and the cost of the technological solutions in order to choose the less expensive combination which guarantees the minimum reliability level required for such system. Generally, this cost management approach arises at the system design step, for any system: a product, a production tool, a detection system or a safety one for example (Zeblah et al., 2009). A system is competitive if it answers to the requirements of its user and at the slightest expense. It means that at the design step, we have not only to answer to the functionalities requirements, but also to consider reliability and expense criteria.

The issue of this paper is a reliability allocation problem. A lot of authors as (Tzafesta, 1980), (Tillman et al., 1980; Misra, 1986; Kuo & Prasad, 2000; Kuo et al., 2001) have proposed classifications according to several criteria, as the system type (repairable, not repairable, series, parallel...) for example. The reliability optimization problems are NP-hard (Chern, 1992), which means we cannot compute the optimal solution in polynomial time. (Yalaoui et al., 2005b) compute the time complexity of the enumeration of all the solutions of such a problem and show that it is better to use an approximation method for real life problems.

In reliability allocation studies, two different approaches can be distinguished according to the values nature of components reliability (Yalaoui et al., 2004). In the continuous case, components reliability values may be any real value between 0 and 1 (Elegebede et al., 2003; Yalaoui et al., 2005a). In the discrete case, components reliability values may only take their value in a finite set of values between 0 and 1 (Yalaoui et al., 2005b; Aneja et al., 2004; Yalaoui et al., 2005c). In this paper, we are interested in the discrete case, which corresponds to the availability market constraint. As far as the use of ant colony optimization (ACO) for the design problem with reliability, (Nahas & Nourelfath, 2005) developed a specific method used for series systems. They studied this system, maximizing its reliability under cost constraints. They considered a system composed of several components in series. For each component, it exits different available technologies with different costs, weights, and reliabilities. The design problem studied in Nahas and Nourelfath (2005) is to choose the best components combination in order to maximize the reliability for a given cost.