Component-Wise Shewhart-CUSUM Monitoring for Progressively Type-II Censored Weibull Lifetime Processes
- 1Department of Statistics, Faculty of Science, Fırat University, 23119 Elazig, Turkey
Abstract
Progressive Type-II censoring presents important challenges for monitoring lifetime processes, particularly when distributional changes affect multiple parameters. This study proposes a component-wise combined Shewhart–CUSUM monitoring framework for progressively Type-II censored Weibull lifetime processes, with minimum density power divergence estimation (MDPDE) incorporated as an optional robust estimation component. The Weibull scale and shape estimates are transformed into finite-sample signed normal scores using Monte Carlo reference distributions, enabling directional monitoring of individual parameter changes. A two-sided Shewhart mechanism and four directional CUSUM statistics are jointly calibrated to achieve a nominal in-control average run length of approximately 370. Simulation results under early, uniform, and late progressive censoring demonstrate effective detection of scale, shape, and simultaneous parameter changes. The CUSUM component provides sensitivity to moderate persistent shifts, whereas the Shewhart component contributes to the immediate detection of large transient departures. An external comparison with an existing EWMA-MAX chart shows shorter out-of-control average run lengths for the proposed procedure across the 36 investigated configurations. Robustness analyses indicate that positive MDPDE tuning can improve shape-parameter estimation but does not consistently enhance the monitoring performance relative to maximum likelihood estimation. Its benefits depend on the censoring scheme, contamination direction, and affected parameter. The framework is further illustrated using Kevlar 49/epoxy stress-rupture data, where an immediate Shewhart signal is followed by directional CUSUM signals confirming persistent distributional changes. Overall, the proposed approach provides a censoring-aware and interpretable monitoring framework that combines complementary detection mechanisms with an optional, condition-dependent robust estimation component.
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BibTeX
@article{calık2026componentwise,
title = {{Component-Wise Shewhart-CUSUM Monitoring for Progressively Type-II Censored Weibull Lifetime Processes}},
author = {Sinan Çalık and Ayse Bugatekin},
journal = {Mathematics},
year = {2026},
month = nov,
doi = {10.3390/math14214103},
url = {https://www.mdpi.com/2227-7390/14/21/4103},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Component-Wise Shewhart-CUSUM Monitoring for Progressively Type-II Censored Weibull Lifetime Processes
AU - Sinan Çalık
AU - Ayse Bugatekin
PY - 2026
DA - 2026/11/09
JO - Mathematics
DO - 10.3390/math14214103
UR - https://www.mdpi.com/2227-7390/14/21/4103
AB - Progressive Type-II censoring presents important challenges for monitoring lifetime processes, particularly when distributional changes affect multiple parameters. This study proposes a component-wise combined Shewhart–CUSUM monitoring framework for progressively Type-II censored Weibull lifetime processes, with minimum density power divergence estimation (MDPDE) incorporated as an optional robust estimation component. The Weibull scale and shape estimates are transformed into finite-sample signed normal scores using Monte Carlo reference distributions, enabling directional monitoring of individual parameter changes. A two-sided Shewhart mechanism and four directional CUSUM statistics are jointly calibrated to achieve a nominal in-control average run length of approximately 370. Simulation results under early, uniform, and late progressive censoring demonstrate effective detection of scale, shape, and simultaneous parameter changes. The CUSUM component provides sensitivity to moderate persistent shifts, whereas the Shewhart component contributes to the immediate detection of large transient departures. An external comparison with an existing EWMA-MAX chart shows shorter out-of-control average run lengths for the proposed procedure across the 36 investigated configurations. Robustness analyses indicate that positive MDPDE tuning can improve shape-parameter estimation but does not consistently enhance the monitoring performance relative to maximum likelihood estimation. Its benefits depend on the censoring scheme, contamination direction, and affected parameter. The framework is further illustrated using Kevlar 49/epoxy stress-rupture data, where an immediate Shewhart signal is followed by directional CUSUM signals confirming persistent distributional changes. Overall, the proposed approach provides a censoring-aware and interpretable monitoring framework that combines complementary detection mechanisms with an optional, condition-dependent robust estimation component.
SN - 2227-7390
ER -