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This thesis investigates methods for assessing reliability equivalence factors for several common systems that comprise independent components or subsystems. We consider improving the reliability of the systems by (a) a reduction method and (b) several duplication methods: (i) hot duplication; (ii) cold duplication with perfect switching; (iii) cold duplication with imperfect switching. Two measures for comparing system improvements are considered in this study, survival reliability equivalence factors and mean reliability equivalence factors.\ud \ud We apply our study to: (1) some simple systems including parallel-series and series-parallel systems, with flexible lifetime distributions including generalized quadratic failure rate and exponentiated Weibull lifetime distributions; (2) networks and complex systems with multiple types of components. We choose the exponentiated Weibull and generalized quadratic failure rate distributions because they are flexible and enable comparisons with other reliability equivalence studies.\ud \ud We use the concept of survival signature to derive the reliability equivalence factors for any coherent system with any structure and with different lifetime distributions. In order to implement this approach, we use the ReliabilityTheory R package to derive survival reliability equivalence factors and mean reliability equivalence factors for networks and complex systems with multiple types of components.\ud \ud Numerical examples for simple and complex systems are presented, to illustrate how to apply the theoretical results and demonstrate the relative benefits of various system improvements. We explain and discuss the results\ud obtained by presenting summary tables and figures, before presenting conclusions and recommendations that arise from this study. In particular, we deduce that considerable advances in reliability equivalence testing are made possible by specifying and analysing the survival signature, especially for the increasingly common context and practice of modelling networks and complex systems. |
