ويژگي هاي تصادفي و استنباط آماري براي سيستم هاي تسهيم بار

چكيده انگليسي :

Stochastic Properties and Statistical Inference for Load Sharing Systems Mohaddeseh Ghafoorifard m ghafoorifard@math iut ac ir January 20 2019 M S Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Maryam Kelkinnam m kelkinnama@cc iut ac irAdvisor Dr Zahra Saberi z saberi@cc iut ac ir2000 MSC 90B25 62K10 62N05 Keywords Load sharing system Stochastic orders Generalized confidence interval Parametric bootstrap Maxi mum likelihood estimation Redundancy allocation Abstract One of the most basic purposes in reliability engineering is modelling the reliability of systems For this goal itshould be given special attention to the performance of the components and environmental conditions of the system One of the important features of the systems that must be considered in modelling the reliability is the dependencestructure between the components In contrast to the independence assumption of the components in the literature in many real applications the failure of a component affects on the alive components In recent decades it has beenpaid attention to dependent failures in a system and in this regard different models have been proposed to assess thereliability of systems In the reliability engineering a load sharing system is a system in which the induced load isshared by the operating components in the system during its operation In the other words if one component failsthen the working components will have to bear the load of failed component In this case the reliability of survivingcomponents are strongly affected due to increased load e g stress current etc As an example in a suspensionbridge cables are used to share the total stress of the bridge However if any of the cables brake the remaining cablesshare the same stress In the literature for the analysis of the load sharing models often the lifetime of the components are considered asexponential Weibull and log normal distributions Obviously in practice we come across with the systems whosefailure mechanism cannot be specified by the above mentioned failure time distributions Therefore it seems nec essary to use some more flexible lifetime distributions The lifetime distributions with bathtub shaped hazard ratefunctions have attracted the attention of many researchers as the lifetimes of various industrial items including elec trical and mechanical products In this regard for constructing the load sharing model a modified Weibull lifetimedistribution is used After modelling the reliability of the system with load sharing model one of the most importantproblems is the statistical inference on the parameters of the model which can be done as parametric and nonpara metric approaches and have been investigated by many authors In this thesis to estimate the parameters of the model the maximum likelihood method and also the bootstrap method is used At the continue in Chapter 3 using the concept of generalized pivotal quantity the interval estimation of the parametersof the exponential distribution as the lifetime distribution of system components are obtained This type of confidenceintervals in addition to the model parameters can be applied for the reliability function the mean time to failure andhazard rate function of the system In reliability engineering a common technique to improve the system reliabilityis using the redundancy at the system One of the most important problems in the redundancy allocation is determining how to use redundant componentswhich leads to the optimal maximal reliability In Chapter 4 under the assumption that the original and redundantcomponents constitute a load sharing sub system the problem of optimal redundancy allocation to the system isinvestigated In order to determine the better allocation we compare stochastically the systems with respect to theusual stochastic order

غفوري فرد، محدثه

ويژگي هاي تصادفي و استنباط آماري براي سيستم هاي تسهيم بار

سيستم تسهيم بار , ترتيب هاي تصادفي , فاصله اطمينان تعميم يافته , بوت استرپ پارامتري , برآورد ماكسيمم درستنمايي , تخصيص اجزاء مازاد