Generalized fiducial inference for the lower confidence limit of reliability based on Weibull distribution

Abstract

Reliability performance, especially the lower confidence limit of reliability, plays an important role in reliability assessment, and it is also of concern to researchers and engineers. In this article, a novel estimate of the lower confidence limit of the reliability for two-parameter Weibull distribution is proposed based on the generalized fiducial inference. The corresponding adaptive Metropolis-Hastings within Gibbs algorithm is provided to analyze the generalized fiducial lower confidence limit. The proposed lower confidence limit of the reliability is compared with that from frequentist method. In addition, this novel procedure is generalized to the series system and the parallel system which consists of identical Weibull components. Simulation results show that the proposed generalized fiducial lower confidence limit is more applicable than the frequentist method, especially for the case of small sample size. Finally, the MOS transistor lifetime data is used to illustrate the new procedure.