Cold Standby System
Consider a cold standby system with two identical components. Initially, one component is working while the other is in standby. The failure rate of the standby component is zero. After a failure of the working component, the standby component will become operational. The system reaches a failed state after the failure of the second component. Figure 8-12 shows the state transition diagram for this system.
Following the previous procedures:
Similarly, reliability of an -component cold standby system (1 online,n-1 in standby) is:
Therefore:
The same procedure can be extended to a -out-of- cold standby system where initially there are k units in operation and (n-k) units in standby:
Therefore:
Consider a 1-out-of- cold standby system with non-identical units. The failure rate of component I is λI. Figure 8-13 shows the state transition diagram for this system.
Following the previous procedures, the reliability of the system is:
After simplification, the MTTF of the system is:
 | It should be noted that if n is large (preferably all failure rates are almost equal), then the failure time distribution follows the normal distribution with the mean (α) and standard deviation (σ), where: |
Therefore, the reliability of the system is:
Where Φ()is the cumulative distribution function of the standard normal distribution. For additional information, refer to the numeric results in Table 3-2.