Statistical Analysis Of Dependent Geometric Distribution Units Under Masked Data

Geometric distribution is an important discrete distribution.In the actual life,many products measured by the number of times are subject to geometric distribution,so it has a wide range of applications in the field of reliability analysis.And reliability analysis often are achieved by life testing,but because of time and money and other factors,the system life data acquisition are often incomplete.The system life data obtained at this time are called shielded data.Taking into account the complexity of the system,the system components may exist between some kind of association rather than independent of each other.This article is based on this background.The first chapter introduces the background of this topic and the related domestic and foreign literature.As the preliminary knowledge of this article,the second chapter briefly introduces the definition of two-dimensional geometric distribution and its basic properties.In the third chapter,we mainly study the parameter estimation of parallel systems composed of two dependent geometric distribution units under shielded data.Firstly,the basic assumptions of shielded data model in parallel system are given.Then the maximum likelihood function of the system lifetime under the whole sample data is constructed,and the existence of the solution of the maximum likelihood function is explained.Finally,Monte Carlo simulation is used to generate the system lifetime data,and the maximum likelihood estimates are given for different sample data.In the fourth chapter,we mainly study the parameter estimation of three-element string-parallel system in the case of shielded data.The system is connected in parallel by the two dependent units which obey the two-dimensional geometric distribution and then in series with the geometric distribution unit 3.Firstly,the basic assumptions of shielded data model in string-parallel system are given.Then the maximum likelihood function of the system lifetime under the whole sample data is constructed,and the existence of the solution of the maximum likelihood function is explained.Finally,Monte Carlo simulation is used to generate the system lifetime data,and the maximum likelihood estimates are given for different sample data.In the fourth chapter,we mainly study the parameter estimation of three-element parallel series systems in the case of shielded data.The system consists of two dependent units in series,and then with the geometric distribution unit 3 in parallel.Firstly,the basic assumptions of shielded data model in parallel series system are given.Then the maximum likelihood function of the system lifetime under the whole sample data is constructed,and the existence of the solution of the maximum likelihood function is explained.Finally,Monte Carlo simulation is used to generate the system lifetime data,and the maximum likelihood estimates are given for different sample data.