A1256
Title: Monte Carlo estimation of ARL with censored data
Authors: Sungim Lee - Dankook University (Korea, South) [presenting]
Johan Lim - Seoul National University (Korea, South)
Soohyun Ahn - Ajou University (Korea, South)
Abstract: The Average Run Length (ARL) is a central performance measure in statistical process control, yet its estimation via Monte Carlo (MC) simulation can be computationally expensive, especially for time-weighted control charts, such as EWMA and CUSUM. A key difficulty arises from extremely long Run lengths, which are typically discarded in practice, leading to both inefficiency and bias. This issue is revisited from a censoring perspective. Instead of discarding non-signaling iterations, they are treated as censored observations and incorporated into the estimation process. A Type I censoring approach based on a memoryless-Type property is first discussed, and then extended to a more flexible framework using random censoring. The proposed methods leverage the Kaplan-Meier estimator and inverse probability of censoring weighting (IPCW) to obtain reliable estimates of both the ARL and its variability. Numerical results demonstrate substantial gains in efficiency and accuracy compared to conventional MC approaches. This framework provides a simple yet effective way to improve ARL estimation across a wide range of control charts.
