A distributionally-robust bayesian adaptive EWMA chart for joint surveillance of lognormal process location and scale

Abstract

Reliability surveillance of safety-critical systems often involves monitoring positively skewed characteristics, such as failure rates, repair times, or material degradation paths, which are robustly modeled by the lognormal distribution. We propose a Distributionally-Robust Bayesian Adaptive EWMA (DR-BAEWMA) framework for the joint surveillance of the log-scale mean and variance under practical model and information uncertainty. Decisively departing from standard Bayesian charts that assume a perfectly specified likelihood, our architecture integrates a distributional-robustification layer using Wasserstein ambiguity sets to protect online estimates against heavy-tailed contamination and misspecified sensor noise. Operating on the log scale, the method treats process health as a latent variable within a non-stationary state-space formulation, decoupling true signals from instrumentation noise via variance-inflation surrogates derived from distributionally robust optimization (DRO) duality results. Decision-theoretic point estimates under both symmetric squared-error loss (SELF) and asymmetric Linex loss (LLF) are incorporated to support risk-sensitive monitoring priorities integrated into the alarm thresholding. We present an adaptive sampling approach that minimizes a principled cost-delay objective to estimate the optimal inspection effort online in order to account for practical problems. Robust univariate and multivariate alarms are provided by a scalar Max statistic and a multivariate Mahalanobis intensity; control limits are obtained by nested Monte Carlo calibration to guarantee that the framework maintains its specified in-control average run length ( A R L 0 ) under ambiguity and variable information density. Extensive simulation across steady-state, polluted, and cross-distributional regimes demonstrates a significantly reduced worst-case detection time as compared to conventional Bayesian and frequentist EWMA approaches. An industrial semiconductor hard-bake case study is used to illustrate implementation, robustness diagnostics utilizing the information ratio, and the effectiveness of adaptive maintenance-on-demand bursts. For real-time monitoring in safety-critical engineering applications, the framework offers an operationally tractable and mathematically rigorous instrument.