Fuzzy Reliability Of System

In the present practical engineering, we need to give the overall analysis andresearch for the reliability of components and all kinds of systems. All the time, theseare hot points problems, the estimation of the parameters which exists in lifetimedistribution of products, studying the reliability for the un-repairable systems andrepairable systems. The traditional parameter estimation method requires a largenumber of accurate statistical data, but in the real world, the collected data are oftennot sufficient and accurate due to human errors or machine failure. In this case, howto estimate the parameters become a practical problem. With the development ofresearch for system reliability, people begin to realize that there existence not onlyrandomness but also fuzziness in many practical systems. So the conventional binarystates reliability description has not be adapted to the practical situations. In fact, therandomness and fuzziness often exist in a variety of complex engineering systems atthe same time. Conventional reliability theory has been unable to meet the needs ofthe more and more complex engineering systems. Even in some models, the resultfrom the conventional analysis method does not accord with the actual situation. Nowpeople begin to study the fuzzy reliability by introducing the fuzzy mathematicaltheory into the reliability research.In this paper, we mainly do following some works:(1) We discuss the fuzzy Bayesian estimator for the characteristic lifetime of typicalWeibull distribution based on the reliability of components, considering the fuzzinessof data, we can get the expression of the fuzzy Bayesian estimator for thecharacteristic lifetime by using conventional Bayesian method and fuzzy sets theory.Especially, we give the method to determine the membership function. Finally, wegive a numerical example to illustrate the feasibility of our method.(2) We study the fuzzy reliability for some typical systems, such as series systemand parallel system based on assumption that all components following exponentialdistribution. We study the reliability of system focusing on the fuzzy data. We alsogive a numerical example to explain our method being feasible and valuable in realengineering.(3) We discuss the fuzzy reliability for system based on fuzzy states. Especially,discuss the fuzzy reliability for the interesting liner and circular repairable systems.We also give a numerical example to clarify the rationality of our algorithm comparing fuzzy reliability with conventional reliability. We find that fuzzy reliabilitytheory is more scientific and practical.