Nonparametric Profile Monitoring using Dynamic Probability Control Limits

This article focuses on monitoring nonparametric profile with time‐varying sample sizes and random predictors. Traditional profile monitoring schemes, whose control limits are often determined before the monitoring initiates, are constructed based on perfect knowledge of profile sample sizes and predictors. In practice, however, our foreknowledge about future random sample sizes and predictors is seldom available. An inappropriate assumption or estimation of the sample sizes model and/or predictors distribution function may lead to unexpected performance of traditional control charts. To overcome this problem, we propose a kernel‐based nonparametric profile monitoring scheme which integrates the multivariate exponentially weighted moving average procedure with the probability control limits. The success of the proposed chart lies in the use of dynamic control limits which are determined online, essentially aiming at guaranteeing the conditional probability that the charting statistic exceeds the control limit at present given that there is no alarm before the current time point to meet a pre‐specified false alarm rate. The simulation studies show that the proposed control scheme has good in‐control and out‐of‐control performances under various scenarios of time‐varying sample sizes and random predictors.