الفهرس 
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Abstract
Reliability technology has a potentially wide range of application areas such as environmental protection, optimization of maintenance operation, engineering design and etc. For many realistic reliability and hazard rates problems for which different models may be applied. In various industrial and other setups, the methods of improving reliability system and analysis the hazard rates were investigated by different references. The objective of research development mathematical and statistics models to compute reliability and analysis the hazard rate of some system and application of the developed mathematical model on simplified case study and analysis of the obtained results. The general content of the thesis are presented in five chapters that are devoted to present: The first chapter includes some definitions and basic concepts in reliability. The objective of chapter two is to study the exponentiated generalized Weibull-Gompertz distribution EGWGD which generalizes a lot of distributions. Several properties of the EGWGD such as reversed (hazard) function, moments, maximum likelihood estimation, mean residual (past) lifetime, stress-strength model, MTTF, MTTR, MTBF, maintainability and availability are studied in this chapter. A real data set is analyzed and it is observed that the present distribution can provide a better fit than some other very well-known distributions. Our aim in the third chapter is to study the mixture of two exponentiated generalized Weibull-Gompertz distribution (MEGWGD) using a mixing parameter where , which generalizes a lot of distributions. Several properties of the MEGWGD such as reversed (hazard) function, moments, maximum likelihood estimation, mean residual (past) lifetime, MTTF, MTTR, MTBF, maintainability and availability are studied. A real data set is analyzed. It is observed that the present distribution can provide a better fit than some other very well-known distributions. In chapter four we introduce a bivariate exponentiated generalized Weibull-Gompertz distribution based on Marshall-Olkin method. We study its statistical and reliability properties including moments, maximum likelihood estimators, the joint reversed (hazard) function and the joint mean waiting time. A real data set is analyzed, which show that the bivariate exponentiated generalized Weibull-Gompertz distribution can be used quite effectively in fitting and analyzing real lifetime data. Finally, in chapter five we study analysis of Weibull-Gompertz distribution based on type II censoring samples and upper record values. Two different real data sets are analyzed and obtained that the present model provides a good fit to this data.