fails to traverse the system if it fails to penetrate C 6. From Fig. 32, the number of such
particles is 723,879 - 217,164 = 506,715. Thus, the number of particles that traverse the
system - 1,000,000 - 506,715 = 493,285.
Related Calculations: The moving-particle method discloses certain principles
very clearly. For example, assume that a simple composite system has components in se-
ries. To traverse the system, a particle must penetrate all components, and therefore the
resistance of each component contributes to the resistance of the system. Thus, the resist-
ance of the system exceeds that of any component, and the reliability of the system is less
than that of any component. Now assume that a simple composite system has components
in parallel. These components offer alternative paths for the moving particles, and there-
fore the reliability of the system exceeds that of any component.
ANALYSIS OF SYSTEM WITH SAFEGUARD
BY CONVENTIONAL METHOD
A system is constructed by arranging the components in the manner shown in Fig. 33, and
the reliability of each component for a given time t is recorded in the drawing. Find the
reliability of the system for time t.
Calculation Procedure:
- Identify the types of failure
The system operates if any of the following pairs of components operate: C 1 , and C 4 ; C 2
and C 4 ; C 2 and C 5 ; C 3 and C 5. Thus, if C 1 and C 3 both fail, the system continues to oper-
ate through C 2 , and therefore C 2 is a safeguard. The reliability of the system can be found
most simply by determining the probability that the system will fail.
There are several modes of potential failure, but they can all be encompassed within
two broad types. A type 1 failure occurs if each of the following events occurs: (a) C 2
fails; (b) either C 1 or C 4 fails, or both fail; (c) either C 3 or C 5 fails, or both fail. A type 2
failure occurs if each of the following events occurs: (a) C 5 operates; (b) C 4 fails; (c) C 5
fails.
FIGURE 33