Higher order normal approximation approach for system reliability assessment

In industry and engineering, reliability analysis of complex systems is one of the most concerning problems. System reliability depends on the reliability of components and system structure. Due to high testing costs, only component data is available and sample sizes are strictly limited. In this article, we describe a new form of WCF expansion for determining the confidence bounds of system reliability. WCF expansion is a higher order normal approximate approach to deal with confidence interval associated with small sample. The Weibull distribution is the most widely used lifetime model in engineering. However, statistical analysis of the Weibull distribution is difficult because of the complicated expression of its distribution function. We present an approach to determine the point estimation of reliability of the Weibull distribution, relying on the reliability parameter. We then apply this property to determine the confidence bounds for system reliability. Our method leads to a better performance and an accurate confidence lower bound for system reliability. Some simulation studies are presented to demonstrate the applications of our method.