Masked Data Of Three Unit Mixed System Reliability Analysis

In the life test, the real failure causes of the system are oftenblocked due to various factors, such as loss of diagnostic tool, datarecording error, time limit, and so on, the data obtained under thissituation is called masked data. In recent years, many scholars havedone a lot of statistical research and analysis on this type of data,mainly focusing on the maximum likelihood estimate, bayesian estimateand interval estimate according to the various distributions that the unitobeys in a series system or a parallel system when masking occurs. Thisarticle is a combination of series system and parallel system. Whilemasking occurs, the maximum likelihood estimation and approximateinterval estimation of the parameters of the three-unit parallel-seriessystems and series-parallel systems whose failure rate is a constant or alinear function that passes through the origin of the system are bothderived, respectively.Chapter one focuses mainly on the introduction of researchbackgrounds and some basic assumptions of the model which will bediscussed in the later essay.Chapter two deduces the maximum likelihood functions of athree-unit parallel-series system whose failure rate is either a constant orlinear function that passes through the origin of the system withcomplete or censored samples when masking occurs. Besides, weprove the uniqueness of the solution to the maximum likelihoodequations under the complete sample case. Since the proof of theuniqueness of the solution to the maximum likelihood equation can’t begiven with the censored samples, there is a demonstration of theuniqueness of the solution to the likelihood equation by drawing. In theend, results of1000simulation of maximum likelihood estimate of theparameters and the approximate interval estimation are listed through Monte-Carlo simulation under all kinds of situations.Chapter three carries a research on the maximum likelihoodfunctions of a series-parallel system with three main units whose failurerate is either a constant or linear function that passes through the originof the system with complete sample or censored samples based onmasked data. In the present essay, we also show the proof of theuniqueness of solution to the maximum likelihood equations. Finally,results of1000simulation of the maximum likelihood estimate of theparameters and the approximate interval estimation are providedunder different circumstances by using Monte-Carlo simulation.