Second-order WCF Approximation For System Reliability Assessment

In the field of reliability engineering, the quantification of a complex system’s reliability is a critical challenge. Basically, the system reliability is affected by the lifetime distributions of components and the structure of the system. We focus on the situation where only the small-size components data are available, which is quite common because of the expensive testing cost and long testing time. Under such circumstances, the traditional methods might not work, so a more accurate approach is needed. The Winterbottom-extended Cornish–Fisher (WCF) expansion, as a distribution approximation technique, offers a superior rate of convergence over the delta method, thereby rendering it adept at handling scenarios characterized by small sample sizes. We make some further research and derive the second-order WCF expansion for the system reliability assessment. Experimental results demonstrate that our method can estimate the lower limit confidence of system reliability accurately and swiftly, even though the test data are rare.