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Abstract
ABSTRACT br Reliability theory has certainly played an important role in industrial and br system engineering. Customers and users are always looking for high quality br and long life products or systems. Therefor, continuous improvement of prod- br ucts or systems becomes essential and even critical. The term ” reliability ” br can be de.ned as the ability of a product or system to perform over a period br of time according to design speci.cations or according to user expectations. br Longer life is identi.ed with greater reliability. br In measuring reliability, we are observing lifetimes of products or systems br of interest. In -#111;-#114;-#100;-#101;-#114; to gain a sound knowledge about product or system br failure-time distributions, life testing and reliability experiments are carried br out before ( and while) products are put on the market or system are used. br Life-testing experimentation is a practical way to determine the product relia- br bility and product quality. A life-testing experiment is one in which a sample br of the item of interest are subjected to stresses and environmental conditions br that epitomize the intended operating conditions. During the life-test, succes- br sive times to failure are noted and lifetime data are collected. These life time br data are used to estimate certain parameters, to make predictions, or to make br decisions on accepting a batch of items. Life-testing is useful in many indus- br trial environments including automobile, materials, telecommunications, and br electronics industries. br In a life-testing experiment, if all the items under test are observed until br failure, the life-test is said to be a complete life test. However, in -#111;-#114;-#100;-#101;-#114; to save br on test time or to save on the number of test items, it is common that not all br the items under test will be observed until failure in an industrial setting. In br other words, some of the test items will be withdrawn or removed -#102;-#114;-#111;-#109; the br life test. Such a life test is said to be a censored-sample life test. br Let X be a set of n generalized -#111;-#114;-#100;-#101;-#114; statistics -#102;-#114;-#111;-#109; the class of dis- br tributions : In this thesis we study three problems related to the class of br distributions as well as the .nite mixture of it based on X. br The .rst problem is about some recurrence relations for joint moment gen.-