## Reliability using empiricalBayesian and multiple Bayesian methods.

Reliability optimization provides help to the reliability engineer to nd the nest way to increase the reliability of the system. For asystem design with high reliability and low requirement, the systemdesigner can adopt series and parallel technique to improve thereliability of the system with available constraints such as cost,weight etc. The constraint of reliability problems can be involvedin uncertain factors and it can be represented by fuzzy number.Shi et al 9 investigated the point estimation of the reliabilityperformances for a cold standby series system by using empiricalBayesian and multiple Bayesian methods. Nabil Nahas et al 6discussed an application of ant system in a reliability to maximizethe system reliability for a series system subject to the systembudget.Yuan et al 11 and Benjamin Epstein et al 2 have applieddi erent techniques and solutions on series system in di erentenvironment.Abdul Razak at al 1 presented the parallel system model toevaluate the maximum reliability using co-ecient of Variance foreach membership function. Ruan and Sun 8 presented an exactmethod for cost minimization problem in series reliability systemwith multiple component choices. Mahapatra et al 5 presentedfuzzy reliability problem of series system model through fuzzyparametric geometric programming using max-min and max additiveoperator. Sung et al 10 presented a reliability optimization problemsfor a series system with multiple-choice to maximize the systemreliability subject to the budget of the system. Ezzatallah et al3 analyzed reliability of the fuzzy system of a series and parallelsystem, using fuzzy con dence interval. Lee et al 4 analyzed thereliability of a parallel system using (; p) interval valued fuzzynumbers.This paper is constructed as follows. Section 2 gives the notationsand fuzzy mathematics prerequisites. Section 3 gives themathematical formulation in crisp model and fuzzy model. Section4 describes the mathematical analysis. Section 5 gives the solutionprocedure for the series system models. Section 6 illustrates theabove constructed model for parallel system. In section 7, conclusionhas been discussed.