Reliability: Modeling, Prediction, and Optimization

CHAPTER 7

Modeling and Analysis of Multi-Component Systems

7.1 INTRODUCTION

The illustrative examples of Section 1.2 reveal that even very simple products can be decomposed into several parts. For complex systems, the number of parts may be very much larger, and in Section 1.2 a multilevel approach to decomposition of such systems was suggested. The number of levels that is appropriate depends on the system (or product) under consideration. The performance of the system depends on the state of the system (working, failed, or in one of several partially failed states) and this in turn depends on the state (working/failed) of the various components. By a component we mean a unit at one of the lower levels—for example, a part, assembly, or subsystem. The focus of this chapter is on the modeling of failures in multicomponent systems.

One can model system failures in several different ways. We first discuss the black-box approach, where the state of the system is described either in terms of two states (working/failed) or more than two states (allowing for one or more partially failed states) without explicitly linking them to the components of the system. Following this, we discuss the white-box approach, where we model the state of the system specifically in terms of the states of the various components of the system. We confine our attention to the case where each component is characterized by two states (working/failed), as discussed in Chapter 4. One can model the state of each ...