System Reliability Estimation via Shrinkage

In a coherent reliability system composed of multiple components configured according to a specific structure function, the distribution of system time to failure, or system lifetime, is often of primary interest. Accurate estimation of system reliability is critical in a wide range of engineering and industrial applications, forming decisions in system design, maintenance planning, and risk assessment. The system lifetime distribution can be estimated directly using the observed system failure times. However, when component-level lifetime data is available, it can yield improved estimates of system reliability. In this work, we demonstrate that under nonparametric assumptions about the component time-to-failure distributions, traditional estimators such as the Product-Limit Estimator (PLE) can be further improved under specific loss functions. We propose a novel methodology that enhances the nonparametric system reliability estimation through a shrinkage transformation applied to component-level estimators. This shrinkage approach leads to improved efficiency in estimating system reliability.