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System Reliability [Rs (t)]
This is an element or a characteristic that describe how good a system or a device is. Known types of system configurations are either;
Series system
Serial systems are constructed in such a way that if, one of the system's device fails the whole system fails. For a Serial system to be successful, the individual system components must be fully functioning. For example, in the diagram below, if components 2 has malfunctioned, the entire system is said to be faulty.
Rs (t) = R1 *R2*…….*Rn
Rs (t) = R [Rj], if every j = 1
  1. Parallel Systems
In this setup the system components are configured in I such a way that, if a single device fails, the system will continue to operate. Thus, reliability is higher than the series system configuration. In the system below if, component 2 fails the whole system will work eventually. Thus, the system is said to be highly available.

Rs (t) = 1-(1-R1) * (1-R2) * …… * (1-Rn).
Or if the individual components are identical we have;

Rs (t) = 1-[1 - R]n
  2. Combining Configurations.
Combining Configurations.
These are systems constructed by combining a number of parallel and serial configurations. The only process one can obtain such a system reliability, is by pulling down the system in several subsystem and dealing with the calculations as separate systems.
After you have obtained your values. Reconstruct the system using either parallel or serial procedures into the previous system.

Assignment 1
Calculate the resultant reliability if each component reliability in the system is 99%
Here we have to systems each having two components. Each component in the system is connected parallel to each other. But the individual systems are connected in series i.e. System (1, 3) is connected in series with the system (1, 4). Thus;
Rs (t) =1-[(1-R1)*(1-R3)] + 1-[(1-R2)*(1-R4)
Rs (t) =1-[0.01*0.01] +1-[0.01*0. [01]
=0.9999+0.9999
Rs=1.9998 [at time t]
The other reason the system is...