A COMPARATIVE ANALYSIS OF RELIABILITY AND AVAILABILITY OF A DEGRADED THREE-UNIT REDUNDANT SYSTEM UNDER VARIOUS DISTRIBUTION

Abstract

For current high reliability systems, particularly those with redundancy and repair, predicting system performance over time is of prime importance. The classical reliability modelling by means of the exponential distribution does frequently not reflect realistic failure and up-repair behaviour. A comparative study of three statistical distributions such as Exponential, Weibull and Gamma to estimate the system reliability and availability under different transition states has discussed for a series type three-units system, which operates based on degraded unit concept and the presence of a stand-unit. The degradation for a unit takes place in two modes, firstly degraded to 70-75% and further to 50%.  A detailed state-transition model is developed, incorporating full working, degraded, and failed states, with transitions governed by failure and repair rates. Each distribution is applied to model time-dependent behaviours of system components, including transitions from full functionality to standby, degradation, and complete failure. The exponential distribution, mathematically convenient as it is, requires constant failure rates and it often produces unreasonably low reliability predictions. Weibull distribution includes shape and scale as parameters in order to include the aspect of aging and repair and predict a more gradual and realistic degradation curve. The accumulated failure times are modelled by a Gamma distribution and the framework is extended to systems with multiple series failure processes. Overall, this study demonstrates that while exponential models are computationally efficient, they are inadequate for capturing complex system dynamics. The Weibull distribution offers a balance between realism and tractability, making it the preferred approach for reliability engineering in systems with repair, redundancy, and aging components. The insights gained from this comparison can guide the selection of appropriate modelling techniques for accurate performance assessment of safety-critical systems.