Redundancy And Reliability

Conventional design with 100% redundancy though improves reliability but includes high capital and operation cost. At times implementing the reliability engineering practices we can achieve the same degree of reliability with lesser capital and operation cost.?

American Society of Quality defines Reliability as the probability that a product, system, or service will perform its intended function adequately for a specified period of time, or will operate in a defined environment without failure.

System reliability is dependent upon following factors.

1. Reliability of sub-systems and individual components of the system.

2. Manner in which sub-systems and components are arranged in the system

A system components/subsystem is normally configured in mixture of series or parallel based on the component/subsystem reliability. Let us understand its applicability to system design.

Though it has a universal applicability but for better understanding let us consider a system generating 600cfm dry compressed of air consisting of air compressor, desiccant dryer, filter and dry air receiver.

Series configuration:

In series configuration elements or components are arranged in a series. Figure (a) shows a system consisting of ‘n’ units which are connected in series. For the successful operation of the system it is necessary that all ‘n’ units function satisfactorily. If the successful operation of each unit is independent of the successful operation of the remaining units.

then system reliability is

where, ?is the reliability of the first unit, , reliability of the second unit and so on. So, system reliability will be worse than the poorest component in the system. For example, a compressed air system with compressor reliability of 0.95 and a desiccant dryer of 0.98 or with a refrigerated dryer with 0.85 reliability, the system reliability will be 0.95x 0.98= 0.93 with desiccant dryer and the reliability with refrigerated dryer would be 0.95x.85 = 0.80.

Parallel configuration:

In parallel configuration elements or components are arranged in a parallel. Figure shows a system consisting of n units which are connected in parallel. In parallel configuration, satisfactory functioning of any one of the elements leads the successful operation of the system.

Redundancy is the existence of more than one means for performing a required function. Redundancy does not mean to have duplicate hardware. This involves deliberate creation of new parallel paths in the system. redundancy is a simple method for improving the reliability of a system when the element reliability cannot be increased.

For example, we can increase the reliability by building redundancy to the system. Considering the above example with an air compressor with 0.95 reliability. The system reliability can be calculated as ??R= 1- [(1-0.95) (1-0.95)] =0.9975 or 99.75%. We can see that with one compressor we had 95% reliability but when we added one in parallel the reliability improved to 99.75%.

Mixed Configuration:

Mixed configuration uses both series and parallel option to maintain the system on fairly higher reliability than the series configuration and maintaining the capital & operation cost lower. This is the most common method use in the industry based on the criticality of the requirement. Usually based on the overall reliability required for the system some components are placed in series (with higher reliability and some are placed in parallel configuration.

Considering above example with compressor of 0.95 and dryer with 0.98 reliability. Let us take compressor on parallel and dryer on series. The system reliability would be

R= [1- {1-0.95} {1-0.95}]x0.98=0.977

The reliability of the system improved to 97.7 % which in series configuration was 93% . If this is acceptable than the capital investment and operation cost saved by opting the mixed configuration is very good.

m out of n configuration:

In order to improve reliability to a good level considering the capital and operating cost simple series and parallel representations are often inadequate. A first generalization, which includes series and parallel systems as extreme cases, is that of “m-out-of-n” systems. These systems fail if m or more out of n components fail. The case m = 1 corresponds to system requires minimum component to achieve the requirement, out of n component. Again, analysis is simpler if the components fail independently with the same probability P. Then, the reliability can be calculated as

Example: The total compressed air demand is 600 cfm and the minimum air required for the plant is 200 cfm average requirement is 400 cfm and peak requirement is 600 cfm. To meet the requirement, we can option like one compressor (series configuration, n=1) with 600 cfm. Two compressor each 600 cfm (parallel configuration,(n+1) n=2), parallel configuration with three compressor n=3 and m=1 and 200 cfm each. Each compressor reliability is 0.95. Let us calculate the reliability of each system.

Configuration 4 gives the lowest reliability while condition 6 gives the highest reliability.

Configuration 3 is most suitable as the capital and operation cost is lower as compared to Configuration 2 and the difference in Reliability is negligible. Most facility falls under this category.

However, in this case we are only covering the minimum demand, but if the demand is for 600 cfm then we should opt for configuration 6.

It is important to note that as we go on increase the m to get certain level of reliability cost increases, therefore it is important for engineer to identify the critical quantity with least impact to plant operation. The optimum design is meeting the critical load with maximum reliability.