Systems Reliability (Series & Parallel System)

SYSTEM RELIABILITY

There are some who believe that the more features a product has the better its quality. While that may be true in some cases, it also depends on how one defines quality. Your perspective might depend on whether you define quality in terms of the frequency with which a product fails, or how long it performs without failure, or all the things the product is able to do, etc. One thing is certain: as products become more complex (fitted with more components and features), the chance that they will develop problems increases. There was a time when a camera was a simple device for taking pictures. You were required to manually load the film, manually advance the film, manually attach the flash, point, and shoot with the click of a button. Today, the camera comes with a 100- page document that tells the reader about dozens of components and features. Modern features include an autoloading device, built-in-flash, auto film advance, autofocus, photo date, distance adjustment, light adjustment, etc. The basic cell phone was a device for making and receiving phone calls. Today, some cell phones are capable of text messaging, producing and sending digital pictures, and providing access to the Internet. The reliability of these systems is ultimately affected by the number of components in the systems. The reliability of the entire system will also be affected by the manner in which the components are arranged. Components are arranged in series, parallel, or a combination. Figure illustrates the various arrangements. Note that the “R_s” values are the probability that the components will work. When components are arranged in series, the reliability of the system is the product of the reliability of the individual components. For the arrangement shown in Figure, the reliability of the system, Rs, is computed as follows:

Note that the reliability of the system, R_s, is lower than the individual reliabilities of the components. When a system is arranged in series, if a component does not function, the entire system does not work. For the arrangement shown in Figure, the components are arranged in parallel. In this case, if a  component does not function, the component continues to function using another component until all parallel components fail. Thus, for parallel components, the system reliability is determined as follows:

Or in Other Words

Systems Reliability

(1) System connected in series

(2) System connected in parallel

System connected in series follows a multiplication law of probability