Читать книгу Reliability Analysis, Safety Assessment and Optimization - Enrico Zio - Страница 34

In a series system, all components must operate successfully for the system to function or operate successfully. It implies that the failure of any component will cause the entire system to fail. The reliability block diagram of a series system is shown in Figure 1.8.

Figure 1.8 Reliability block diagram of a series system.

Let Ri(t) be the reliability of the ith component, i=1,2,…,n,, and Rs(t) be the reliability of the system. Let xi be the event that the ith component is operational and let x be the event that indicates system is operational. The reliability of the series system can be calculated by

(1.46)

Assume all the components in the series system are independent; if so, the reliability of the system can be expressed as

(1.47)

Considering that the component reliability is a number between 0 and 1, we have the following relationship

(1.48)