Reliability Analysis Of Four-cell Hybrid Systems

In the life test, the real failure causes of system are always blocked due to data recording error,diagnostic tool, time limit, lack of research funding and so on, the data obtained under thissituation is called masked data. Many scholars at home and abroad have done a lot of statisticalresearch and analysis on this type of data due to Usher and Hodgson who first put forward it since1988. They focused on the units in a series system or parallel system when masking occurs, andunits themselves obey Normal distribution, Exponential distribution, Weibull distribution andmany other distributions, their major work is providing the Bayesian estimation, intervalestimation, approximate interval estimation, moment estimation, and maximum likelihoodestimation of the parameters of parallel-series systems and series-parallel system whose failure isa constant, a linear function or some other forms of functions. In this essay, we mainly analysis allkinds of four-unit hybrid system, the maximum likelihood function whose failure is either aconstant or linear function that passes through the origin of the system with complete or censoredsamples when masking occurs.In the first chapter, we mainly focus on the introduction of research backgrounds and somebasic assumptions of the model which will be discussed in the later essay. Afterwards all kinds ofsituation of four-unit hybrid system are listed.From chapter two to chapter seven, we discuss six different situations of four-unit hybridsystem with masking. We carry a research on the maximum likelihood functions of hybrid systemwith four units whose failure rate is either a constant or linear function that passes through theorigin of the system with complete sample and censored samples based on masked data. In thepresent essay, we also show the proof of the uniqueness of solutions for the maximum likelihoodequations under situation one to situation three with complete sample and censored samples basedon masked data. Finally, results of1000simulations of the maximum likelihood estimate of theparameters and the approximate interval estimation are provided under different circumstances byusing Monte-Carlo simulation. Regarding situation four to situation six, we also list the results ofthe maximum likelihood estimate of the parameters and the approximate interval estimation areprovided under different circumstances.