الفهرس 
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Abstract
The main purpose of this thesis is to improve the reliability of some technical systems.
This dissertation highlights the role of partial differential equations on the study of system reliability and availability. It presents, also, a brief survey ofthe current state of topics in reliability theory related to the work done in this thesis. Moreover, it points out the connection with the corresponding less general problems which have been studied by earlier authors.
The thesis deals with the common form of redundant system, k-out-of-n:G systems, since many critical systems cannot achieve their intended reliability without using redundancy. Moreover, to increase the effectiveness of redundancy units that have failed are renewed, if it is possible. Due to the extreme variation of technical systems, problems in reliability theory are extemely varied. One source of variation is the type of failure; partial failure, common-cause failure, catastrophic failure and degradation failure; which may potentially becomes the dominant contributor to system unavailability. The thesis deals with the four kinds of failure and discuss the effect of repair, warm standby and Bayesian analysis in improving system reliability, availability and mean time to system failure.
The main purpose of this thesis is to improve the reliability of some technical systems.
This dissertation highlights the role of partial differential equations on the study of system reliability and availability. It presents, also, a brief survey ofthe current state of topics in reliability theory related to the work done in this thesis. Moreover, it points out the connection with the corresponding less general problems which have been studied by earlier authors.
The thesis deals with the common form of redundant system, k-out-of-n:G systems, since many critical systems cannot achieve their intended reliability without using redundancy. Moreover, to increase the effectiveness of redundancy units that have failed are renewed, if it is possible. Due to the extreme variation of technical systems, problems in reliability theory are extemely varied. One source of variation is the type of failure; partial failure, common-cause failure, catastrophic failure and degradation failure; which may potentially becomes the dominant contributor to system unavailability. The thesis deals with the four kinds of failure and discuss the effect of repair, warm standby and Bayesian analysis in improving system reliability, availability and mean time to system failure.