© I F.-\C Sto,ha sti, Control Yilniu s, Lithuanian SSR, L'SSR, 1'186 EVALUATION OF SYSTEM'S RELIABILITY WITH A FUZZY PRIOR INFORMATION O. Hryniewicz SYsll'lIIS Rnmnh /11.11111111', .\'l'1I'I'/ska 6, \I'a/sOlI', Po/alld Abstract: The system with a series reliability structure and elements having exponentially distributed life times is considered.The data from life tests for each of the system's elements are known.Moreover, it is assumed that there exists a linear relationship between hazard rates in test and real conditions but the coefficients of proportionality are unknown.However, it is also assumed that their values can be evaluated by experts in the form of fuzzy sets. The method for merging prior in- formation from these experts' assessments and from the life tests into the prior distribution of the whole system's hazard rate is proposed. Closed formulas are obtained for the case of piece-wise linear membership functions of the fuzzy sets representing the experts' evaluations. Keywords. Reliability theorYi statistics, Bayes methodsi Prediction. INTRODUCTION One of the most important problems of re - liability engineering is reliability asse- ssment of systems during the initial stage of their exploitation.The r.wuber of systems to be tested is,as a rule,hardly sufficient for precise estimation of reliability cha- racteristics.Consider for example a system of several elements connected in series whose life-times are exponentia- lly distributed. In this case the system'S life-time is also exponentially distribu- ted.Now,assume that its mean time to failu- re equals b.Then,the variance of the stan- dard maximum likelihood estimator of b is gi.ven by where r is the number of observed failures. Therefore,for reliable system's and small samples the precision of estimation is in- sufficient from the practical point of view. There are two ways which allow us to obtain more accurate estimators of relia- bility: either to produce more failures by applying a more severe stress,increa- sing the amount of total test time etc., or to use prior information to obtain mo- re accurate estimators of the reliability to be evaluated,and from the practical point of view the latter is far more in- teresting than the former.This evaluation is based on the fact that even newly de- signed systems consist of elements whose reliability can be evaluated from previo- us experiments.However,there is one seve- re restriction-these experiments are per- formed in different conditions lelectrical or mechanical stresses,enviroment etc.1 and it does not exist any generally accep- ted method for the transformation of test -l51 results from one condition of test to another, Th.e simplust ,and there- fore widely accepted;method con _ sists in multiplication of certain reliability characteristics le.g. the hazard rate I by some coefficie nts whose values are stress-depen- dent.These coefficients are tabu- lated le.g., in the American Mil i tary Handbook 217 I but t..'1eir application in practice seems to be res tr icted. However ,wey can be evaluated in a more fuzzy form, and then utilized in the procedures of reliability prediction. In the paper we consider the pro- blem of reliability estimation with data from three sources: the tests of the considered system's , the tests of elements the system consists of,and the evaluation of coefficients used for the transfor mation of tests results.We utilize these data to construct the Baye- sian estimator of the system's ha- zard rate which gives a more accu- rate prediction of reliability. GENERAL ASSUMPTIONS suppose that the considered system has a series reliability structure and its N elements have exponentia lly distributed times to failures. Let >-. i' i=l ,2, ..• , N be the hazard rate of the i-th element. Suppose now that there are two ty- pes of tests.First,the whole sy- stem is tested in normal