## Fundamental System Structures

A system is called simple if it can be considered a unit with regard to all relevant reliability and maintenance aspects, in particular with regard to the development, occurrence, and localization of failures, as well as with regard to scheduling, materializing and accounting maintenance measures. This explanation does not exclude that simple systems in practice may

be fairly complicated structures or products. In a large computer network, for instance, the individual computers normally can be regarded as simple systems. In the context of the following sections, simple systems are the components, elements, parts or subsystems of structured (complex ) systems. Knowledge of reliability parameters of their underlying simple systems is a prerequisite for the reliability analysis and maintenance planning of structured systems. In this section, let S be a simple system. We will assume that S can only be in one of the following two states: state 1 (available, operating, functioning), state 0 (unavailable, failed, down). Hence, the indicator variable for the state of the system at time t is a

binary or Boolean variable with range f0; 1g:

z(t) =

1 if S is available at time t 0 otherwise

: (1.1)

This assumption implies that the transition of a system from state 1 into state 0 occurs in negligibly small time, i.e. the system is subjected to sudden failures. The chosen binary range f0; 1g is, of course, arbitrary, but later it will prove a very convenient choice.