Some Applications Of Stochastic Order And Aging Concepts In Reliability Theory

The reliability and safety of a system have become an eternal topic in modern engineering design with the social development and scientific and technological progress. Stochastic orders theory and aging concepts of random variables are also of great interest for having a wide application in such as reliability theory,system safety,survival analysis and other related areas.In this thesis,we will further investigate some applications of stochastic orders and aging concepts in reliability theory.As an important technology in reliability engineering,the standby system has been the focus of attention of both engineers and researchers in the recent two decades. Based on the warm standby system with components having proportional failure rates, we first introduce two important evaluation indices,which characterize the reliability of a warm standby system successfully.Furthermore,to minimize standby cost,we build an optimal model for a warm standby system in terms of standby number and standby time.The optimal standby number and standby time are also derived.The accelerated life testing and degradation model are one of the main topics in reliability theory.Based on the simple additive degradation model,the internal connection between the aging properties of the implied lifetime and the analytical properties of the mean degradation path and the aging properties of the random variation are discussed.The sufficient or necessary conditions for the implied lifetime with specified aging properties are also given.We thus successfully correct some serious mistakes in Bae et al.(2007).Order statistics and sample spacings play important roles in reliability theory, life testing and many other fields.We first conduct stochastic comparisons of order statistics and sample spacings from one sample and two samples when the number of observations is random.Meanwhile,when the sample size is random,the stochastic comparisons of sample spacings involved the usual stochastic order are also developed.At the end of this thesis,we introduce the strong stochastic precedence order. Relationships between strong stochastic precedence order and stochastic precedence order and usual stochastic order are discussed.We then present the properties of strong stochastic precedence order and establish its equivalent characterizations.In addition,we apply strong stochastic precedence order to further study the problem of the redundancy allocation of components.