TABLE OF CONTENTS Chapter 1 focused on the reliability of a single-component system. This chapter focuses on the reliability of systems with more than one component, which are referred to as "multi-component systems".
Whereas in the case of single-component systems the failure in the component implies the failure of the system, this is no longer the case for multi-component systems, at least not automatically. The failure in a multi-component system arises in the wake of the failure in the sub-sets of well-defined components. For example, the failure in one of the four cylinders of a car does not jeopardize its overall working: it works badly, but it still works. On the other hand, the failure of the drive shaft leads to the immobilization of the car.
From this example, it can be observed that the sub-sets of the components, whose simultaneous failures lead to the failure of the system, should be defined exactly. This approach makes use of the Boolean algebra, and more specifically uses the structure function, which translates the functional relationships among the components of the system and its state of failure/working.
Let us consider a binary system with n components: C = {1, ., n}: For each component i, we define a variable x i, with value in {0, 1}, with the following convention:
Let x = ( x 1, x 2, , x n) ? {0, 1} n be the vector describing jointly...
