A mathematical formulation of reliability optimized design

Abstract

The problem of optimization of system reliability through an optimum choice of parallel redundancy has been extensively researched in the literature. Many mathematical techniques have been adapted or developed to solve this integer programming problem, however, because of mathematical complexity few of these are widely known or used by reliability engineers.

It is shown that most systems are designed using hierarchical decomposition, which greatly reduces the complexity of the problem and allows simple bounding and enumeration methods. If the entire problem is called Level 0, the next level down, Level 1, is designed by apportioning the reliability goal among perhaps 3–10 subsystems. At Level 2, we would attempt to meet the apportioned reliability goals by an optimum assignment of redundant components. A set of upper and lower bounds on the number of components are developed which establishes a search space. As feasible candidate combinations are evaluated, the bounds are recomputed, further limiting the search space.

The paper also develops solution techniques for standby redundancy, discusses the component improvement approach, and develops criteria for comparing the efficiency of component improvement with parallel redundancy.

A few examples are analyzed to compare the methods, their complexity, and speed of solution.