Study On Lower Confidence Limits For Reliability Of Complex System Based On Minimal Path

For complex system, the types of subsystems, their quantities, their qualitiesand the manner in which they are arranged all have a direct effect on systemreliability. The statistical inference of general complex system reliability is mainlybased on the data information of subsystems. For general complex system describedby minimal path, the analytical expression of reliability has been derived. This paperfocuses on lower confidence limits of complex system reliability, based on theanalytical expression.Asymptotic Normal Method is the common method for calculating lowerconfidence limits of system reliability, and it is convenient and easy for calculate,but the variance of normal distribution is unknown. Commonly we use its estimatorto substitute, but conventional estimator is unbiased, and consequentially there willbe errors. This paper derives the analytical expressions of unbiased estimator for thisvariance, and improves Asymptotic Normal Method. Simulation results show thatthe improved method is also convenient and is more accurate than the commonmethod.However, when the sample size of subsystem is small, both the AsymptoticNormal Method and improved Asymptotic Normal Method are not accurate enough.WCF Method is a classic way to derive lower confidence limits of parameterfunctions. This paper first gives the formula of the lower confidence limit ofreliability by applying WCF method to all complex system described by the minimalpath. Simulation studies for the Bridge system demonstrate the efficiency of themethod and the superiority compared with other methods.The methods in this paper are not only theoretically significant but also have theresults of estimates which are more accurate than other methods even when thesample size is so small. They are not only for series systems, parallel systems and series-parallel systems, but also for non-series-parallel systems, that means they havewide applicability. In simulation, just input the minimal path matrix and life samplesof subsystems, estimates of variances of estimate and lower confidence limits forsystem reliability can be obtained, so it is convenient for programming.