الفهرس 
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Abstract
In this thesis, we study the concept of reliability equivalence of some simple and complex systems with components having a mixture of different failure rates. Such concept is applied to calculate the reliability equivalence factors of these systems. where the system reliability can be improved by: (i) reducing the failure rates of the system components by this factor; (ii) assuming hot duplications of some system components; (iii) assuming cold duplications of some system components via perfect switches; (v) assuming cold duplications of some system components via imperfect switches. The concept of reliability equivalence is applied to some simple systems such as the single component system and the n-independent and non-identical components series system when the failure rate of each component is presented as a mixture of three constant failure rates. Also, we applied this concept on some complex systems such as the radar system in an aircraft which consists of three independent and non-identical components that are connected neither in series nor in parallel. Finally, we applied the concept of reliability equivalence on an n-components series system when the failure rates of the system components are presented as functions about time t. The thesis contains four chapters and list of references.