The Reliability Under The Fuzzy Environment

With the development of the reliability theory, peoples find that there exist not onlyrandomness but also fuzziness. Thereby, it is important real significant that generalizeordinary events and conventional reliability to fuzzy events and fuzzy reliability respectively.In this paper, we mainly study the reliability of systems, using three different reliabilityapproaches under vague environment.In the first chapter, we introduce mainly related the definition of fuzzy reliability andconceptions, review the originator and development of the fuzzy reliability theory and ourcreature.Under vague environment, it is difficult to obtain the accurate Bayesian estimator undertwo parameters situation. In second chapter, for above problem, we obtain the accurateBayesian estimators of the parameters. For two-parameter normal distribution, we give thejoint priori distribution of two parameters based on normal distribution by the Jeffery’sapproach, and get the joint posteriori distribution of the two parameters. As a result, themarginal distributions of the two parameters are general T distribution and upside Gammadistribution respectively. In final, we can obtain the analytical solutions of the Bayesianestimators of the two parameters.Selection of the membership function is key to the assessment of the fuzzy reliability.On researching fuzzy reliability in third chapter, using fuzzy structure element method wesolve the problem using fuzzy structure element method that selecting membership functionand obtaining the fuzzy reliabilities of the Special Series-parallel System and Parallel-seriessystem. Our approach can prevent human factors which exit in conventional selectingmembership function. We can get fuzzy confidence directly interval of the fuzzy reliability,using the relationship between fuzzy reliabilty and structure element. Such that the solutionis more accurate. Our approach can provide a new way to study the reliability of largecomplex system.In future, using fuzzy conditional probability method, researchers have studiedsuccessfully the fuzzy reliability for n-unit cold standby system and two-unit cold standbysystem and two-unit warm standby system. But they assessment that all componentsfollowing exponential distribution. In forth chapter, we discuss the fuzzy reliability for anew Cold Standby with two categories of components.