Standby Systems with a Switching Device
In the last issue of the HotWire, we discussed the case of a system with standby components where a standby component automatically becomes active in the event of the failure of another component in the configuration. However, in many cases when dealing with standby systems, a switching device is also present and required to switch to the standby component in the event of the failure of the active component (as shown in Figure 1). Therefore under such conditions, the failure properties of the switch must also be included in the analysis. This article discusses the failure properties of the switch as well as their incorporation into the analysis and presents an example of such analysis using the BlockSim 6 software.
In analyzing standby components with a switching device, either or both probabilities can be considered for the switch because, depending on the application, each probability can represent different failure modes. For example, the Switch Probability per Request may represent software related issues or the probability of detecting the failure of an active component and the quiescent reliability may represent wear-out type failures of the switch.
Figure 2: RBD for 2 components in standby configuration
In that example, we assumed perfect switching from standby to active when necessary. In this example, let's examine the effects of including an imperfect switch. Assume that when the active component fails, there is a 90% probability that the switch will transfer from the active component to the standby component. In addition, assume that the switch can also fail due to a wear-out failure mode described by a Weibull distribution with beta = 1.7 and eta=5000. Note: For this example, we will only consider the non-repairable case, i.e. when a component fails, it is not repaired/replaced.
The reliability of the system at some time, t, can be calculated using the following equation:
The BlockSim 6 software (anticipated for release in February 2003) can be used to solve for the reliability of this system. After specifying the block properties of the Active and Standby components (as described in the previous HotWire) the following failure properties can be entered for the switch:
Figure 3: Quiescent failure properties for the standby configuration switch
Figure 4: Probability per Request for the standby configuration switch
Note that there are additional properties that can be specified in BlockSim 6 for a switch, such as Switch Restart Probability, Finite Restarts and Switch Delay Time. These properties are mostly related to repairable systems and are considered in BlockSim 6 only when using simulation. In this article, we are presenting the analytical solution given by Eqn (1) and these properties are ignored.
The results for the analysis with and without incorporating switch reliability are given in the following table:
Rsys(1000) = Rstandby(1000)*Rsw,Q(1000)*Rsw,req = 0.7057*0.9372*0.9 = 0.5952
So the calculated reliability would have been 59.52% instead of 66.35% (from the table above).
In cases where a switch failure mode that causes the standby subsystem to fail is present, then this mode can be modeled as an individual block in series with the standby subsystem. At the same time, however, if the Switch Probability per Request and Quiescent probability need to be incorporated, this must be done as presented in Eqn (1) of this article.
Copyright 2002 ReliaSoft Corporation, ALL RIGHTS RESERVED