MCD–Huber based control chart for contaminated multivariate process monitoring

The SAMEWMA–VSS chart combines support-vector-regression-based adaptive smoothing with a variable sample size within a Mahalanobis-form multivariate EWMA statistic, but neither this mechanism nor the classical multivariate charts it builds on were designed for contaminated data: a single gross measurement error can distort the estimated shift magnitude that drives the chart’s adaptive smoothing constant and sample size, and classical Phase-I moment estimates are well known to suffer from masking under contamination. This paper proposes MCD–Huber SAMEWMA–VSS, which replaces the classical Phase-I mean and covariance with robust minimum covariance determinant (MCD) estimates and replaces each subgroup’s raw contribution with a Huber-weighted one, while retaining the original chart’s SVR-based adaptive smoothing and variable-sample-size mechanisms. An extensive Monte Carlo study compares the proposed chart against the original SAMEWMA–VSS chart and against an Isolation-Forest-weighted (IF-weighted) alternative across clean shifts, gross-error contamination at varying rates and magnitudes, and a range of correlation structures. The results show a clear contrast between the two robust alternatives: the IF-weighted chart’s more aggressive weighting substantially improves contamination resistance but masks genuine large shifts, never signaling at all for the largest shifts examined, whereas MCD–Huber SAMEWMA–VSS achieves a substantial but partial gain in contamination resistance — the in-control average run length under 10% gross-error contamination rises from 27.19 for the original chart to 67.42, still well below the clean target of 370—while retaining detection speed close to the original chart for small and moderate clean shifts (within about 13% up to δ = 1.5), at the cost of slower detection of large shifts (δ ≥ 3), where its ARL levels off near 7. An illustrative NASA IMS bearing feature-based simulation, using real Phase-I vibration-feature statistics as the reference model with simulated Phase-II shifts and contamination, demonstrates the proposed chart’s behavior under both clean and contaminated conditions. Supplementary analyses examine the run-length distribution, the precision of the control limits, the Huber cutoff, the Phase-I sample size and contamination, the delayed-shift metrics FAP τ and CDD τ , dimensions up to 20, serial correlation and computing time.