Reliability Variation Analysis of (m, ni) Order Series-Parallel System under Rayleigh Failure Laws with Addition and Removal of Subsystems
Abstract
A series-parallel system of (m, ni) order has been considered to examine variation in its reliability when some subsystems are added and removed from it. In the original system, ‘x’ subsystems are added in series and ‘y’ subsystems are removed. We determine reliability of the modified system in terms of reliability of the original system (series-parallel system) and variation in reliability due to the changes in subsystems. The failure rates of the components are assumed to follow Rayleigh distribution and accordingly the expressions for variation in reliability are derived. The variation in reliability for a particular series–parallel system of order (4, 3) has been obtained for arbitrary values of the parameters. The linear regression model is fitted for the variation in reliability of this particular system considering the consecutive addition and removal of three subsystems in the original system of order (4, 3). The goodness of fit for reliability variation on the basis of R-square adjusted R- square has been examined considering specific values of the scale & shape parameters and operating time. The results are shown numerically and graphically to depict the behaviour of the variation in reliability. An application of the work is described which can be visualized in a water supply system used in the high-raise buildings.
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