Explain one component redundancy yields higher reliability than unit redundancy. For the general case of an n-component series system, prove that it is true.

MS 57 Assignment Solution | MAINTENANCE MANAGEMENT | One Component Redundancy Yields Higher Reliability…

In order to construct a reliability block diagram, the reliability-wise configuration of the components must be determined. Consequently, the analysis method used for computing the reliability of a system will also depend on the reliability-wise configuration of the components/subsystems. That configuration can be as simple as units arranged in a pure series or parallel configuration.

There can also be systems of combined series/parallel configurations or complex systems that cannot be decomposed into groups of series and parallel configurations. The configuration types considered in this reference include:

• Series configuration. 

• Simple parallel configuration.

• Combined (series and parallel) configuration.

• Complex configuration.

• k-out-of-n parallel configuration.

• Configuration with a load sharing container (presented in Load Sharing).

• Configuration with a standby container (presented in Standby Components).

• Configuration with inherited subdiagrams. Configuration with multi-blocks.

• Configuration with mirrored blocks.

In a series configuration, a failure of any component results in the failure of the entire system. In most cases, when considering complete systems at their basic subsystem level, it is found that these are arranged reliability-wise in a series configuration. For example, a personal computer may consist of four basic subsystems: the motherboard, the hard drive, the power supply, and the processor.

These are reliability-wise in series and a failure of any of these subsystems will cause a system failure. In other words, all of the units in a series system must succeed for the susten to succeed  In the case where the failure of a component affects the failure rates of other components (i.e., the life distribution characteristics of the other components change when one component fails), then the conditional probabilities in the equation above must be considered.

In a series configuration, the component with the least reliability has the biggest effect on the system’s reliability. There is a saying that a chain is only as strong as its weakest link. This is a good example of the effect of a component in a series system. In a chain, all the rings are in series and if any of the rings break, the system fails. In addition, the weakest link in the chain is the one that will break first. The weakest link dictates the strength of the chain in the same way that the weakest component/subsystem dictates the reliability of a series system.

As a result, the reliability of a series system is always less than the reliability of the least reliable component. The number of components is another concern in systems with components connected reliability-wise in series. As the number of components connected in series increases, the system’s reliability decreases.  The following figure illustrates the effect of the number of components arranged reliability-wise in series on the system’s reliability for different component reliability values.

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