Optimal Reliability Allocation with Discrete Cost-Reliability Data for Components

Abstract

This paper addresses the optimal allocation of reliability among components that are to be assembled into a system. While it is a generally accepted notion that a component's cost is an increasing function of its reliability, most research to date adopts exponentially increasing, closed-form functions to relate cost and reliability. However, in practice such functions are often unknown or difficult to construct, and it is often more reasonable to describe cost-reliability relationships via discrete data sets. We consider such situations, where each component is available at several reliability levels with corresponding costs. The design optimization problem results in a nonlinear integer program. Because every system configuration has an equivalent representation as either a series connection of parallel subsystems or a parallel connection of series subsystems, we provide formulations, linear relaxations, and algorithms for these two.

Reliability Allocation

“…A number of publications on reliability allocation consider only the third case, where the optimization problem becomes an integer optimization problem. It becomes a 0-1 optimization problem when choices are discrete and a component from a given list of candidates is either used or not used [2].…”

“…The reliability allocation problem for two basic reliability structures series and parallel can be solved by linearizing the constraints [1,2,7]. In a series system, the constraint is given in equation (2) above, which can be linearized by rewriting it as…”

“…In real systems, the overhead involved will result in a lower level of reliability. In a number of studies, the problem assumes that the reliability of a subsystem can be increased by using a functionally identical component in parallel [2,7]. For parallel systems, the constraint is given by…”

“…In practice, many cases can be complex and may require an iterative approach [1,2,7,12]. Such an approach is also needed if the objective function has multiple objectives and includes both the total cost The optimization methods used in steps 2-5 above can be classified into three approaches [1].…”

A Multi-Objective Multi-State Degraded System to Optimize Maintenance/Repair Costs and System Availability

“…In other words, most of the existing approaches concentrated only on maximizing system availability, and assumed that there is no cost limitation [29][30][31][32][33][34][35][36][37], or considered the cost limitation only as a constraint [38][39][40]. However, it is usually impossible for a single-objective approach to represent a practical problem truly.…”