Recently, control chart methods for monitoring risk-adjusted zero-inflated Poisson (RA-ZIP) processes have gained attention. Existing approaches often assume a constant shock probability pi and ignore cumulative sample information when estimating model parameters, reducing sensitivity to process shifts. This study proposes a likelihood-based EWMA-type control chart for detecting upward or downward shifts in both the Poisson mean theta i and the shock probability pi in RA-ZIP profiles. A memory-type scheme updates the maximum likelihood estimators of the regression parameters from ZIP samples, and a weighted likelihood ratio test (WLRT) statistic is constructed. Monte Carlo simulations compare the proposed WLRT chart with existing WST and GLR charts using the average run length, run length standard deviation, and the relative mean index. The proposed chart shows competitive and often superior sensitivity, particularly for small regression-structure shifts. An application to US flight delay data demonstrates its practical implementation.
Process capability indices (PCIs), essential in manufacturing, engineering, and quality management, quantify process performance, ensuring specification compliance and facilitating continuous improvement. While traditional PCI analysis assumes normality, industrial quality processes often exhibit bounded characteristics violating this assumption. For such scenarios, statistical inference is considered for the PCI given quality characteristics following a bounded lifetime distribution. Classical likelihood-based estimation is discussed under Type-II censoring; the existence and uniqueness of the model parameters are established. For comparison, alternative generalized approach are further proposed to estimate the PCI using constructed pivotal quantities. Finally, extensive simulation studies are conducted to compare the performance of different methods, and two real-life examples are also presented for illustration. The results demonstrate that the proposed generalized methods outperform traditional classical approach in general.
With advancements in production processes and increasing product complexity, inspection operations now depend on numerous challenging measurements. Progress in image acquisition and machine vision has enabled capturing high-resolution images in short intervals, generating massive volumes of data. This study employs a combination of statistical process monitoring and deep learning to analyze image-based data. The process begins with feature extraction using the Shearlet transform, a powerful tool in image processing. A GLR control chart is then applied to evaluate process status, determining whether it is in-control or out-of-control. Performance of the proposed approach is evaluated using metrics including ARL, change-point estimation, and the Dice coefficient. Simulation studies demonstrate the superiority of the Shearlet-based method compared to competing approaches. Beyond detecting process status, three convolutional neural networks (CNNs), AlexNet, GoogLeNet, and ResNet50, are utilized to classify defect types. Transfer learning with ResNet50, pre-trained on ImageNet, assesses robustness against unseen defect classes through the Leave-One-Defect-Out (LODO) protocol. Results show all CNNs achieve high accuracy, with ResNet50 delivering the best performance and strong generalization under LODO evaluation. Finally, to explore transformer-based models for defect classification, the Data-efficient Image Transformer (DeiT-Small/16) is adopted, providing competitive accuracy and enhanced interpretability.
Degradation data contain rich reliability information, providing a novel way to evaluate product reliability, especially for highly reliable products whose lifetime data are scarce. In engineering practice, due to certain unexpected conditions, extreme observations may arise, resulting in heavy-tailed degradation data. However, as a widely used degradation model in the literature, the Wiener process cannot capture the heavy tails, which may cause seriously biased reliability. To this end, we propose a family of heavy-tailed degradation models in this paper, which includes the existing Student-t process model as a member and also produces several new stochastic models. Our models consider the unit-to-unit heterogeneity simultaneously and have nice hierarchical structures that facilitate subsequent inference procedures. Additionally, we develop a simulation-based reliability assessment approach that is applicable to all proposed degradation models. Afterward, we propose an expectation-maximization algorithm to estimate the model parameters. Meanwhile, we conduct a simulation study to verify the proposed estimation method. Finally, our heavy-tailed degradation models are applied to the train wheel data and the infrared light-emitting diode data, and their utility and superiority are clearly demonstrated.
