Study On The Complex System Reliability Confidence Lower Limit Under Incomplete Data

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, this paper focuses on lower confidence limits of complex systemreliability under the incomplete data.Their are many common methods of confidence lower limit for systemreliability, such as the asymptotically normal methods, the advantage of thisapproach is convenient and easy for calculate, but the variance of normaldistribution is unknown. Commonly we use its estimator to substitute, but anyestimates that can’t be accurate, there will be a variety of deviation, andconsequentially there will be errors. However, when the sample size of subsystem issmall, both the Asymptotic Normal Method and improved Asymptotic NormalMethod are not accurate enough. As WCF Method is a classic way to derive lowerconfidence limits of parameter functions. This paper gives the formula of the lowerconfidence limit of reliability under incomplete data analytic expression by applyingWCF method to all complex system described by the minimal path.The methods in this paper are not only theoretically significant but also havethe results 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 andseries-parallel systems, but also for non-series-parallel systems, that means theyhave wide applicability.such as the series-parallel system also has extensiveapplicability. The most important is gives the formula of the lower confidence limitof reliability under incomplete data analytic expression. In simulation, just input theminimal path matrix and life samples of subsystems, estimate and lower confidence limits for system reliability can be obtained, so it is convenient for programming.