ABSTRACT Vibration monitoring sensors are widely used to acquire vibration signals from machinery and structural systems and therefore play an important role in condition monitoring, fault diagnosis, early warning, and operational safety assurance. Accurate lifetime prediction and reliability assessment of such sensors are essential for ensuring the long‐term stability of monitoring systems. However, many conventional accelerated Wiener degradation models assume that the drift parameter alone depends on stress and do not explicitly account for unit‐to‐unit heterogeneity, which may reduce the accuracy of degradation modeling, lifetime extrapolation, and reliability assessment. To address these limitations, this study develops an accelerated degradation model for vibration monitoring sensors based on a Wiener process with random effects. Random effects are introduced into the drift term to characterize unit‐to‐unit variability in degradation rates. Based on the constant acceleration factor principle, the drift and diffusion parameters are linked through a common stress‐dependent acceleration relationship, and a generalized Eyring‐based accelerated degradation model is established. The proposed method is validated using accelerated degradation data of sensor output voltage collected under combined temperature‐vibration stresses. The results show that, compared with a conventional accelerated degradation model, the proposed model provides closer agreement with the empirical reliability estimates and better captures the heterogeneity observed among individual sensors, thereby improving the reliability‐oriented lifetime assessment.
ABSTRACT Several distribution‐free control charts have been developed for joint monitoring of process location and scale under unknown process distributions. Their statistical performance has been well studied, but the economic‐statistical design of such charts has received limited attention. This study develops an economic‐statistical design framework for nonparametric joint location‐scale monitoring. Two Lepage‐type schemes are constructed by combining the van der Waerden statistic with either the Ansari‐Bradley or the Mood statistic. Sample size, sampling interval, and control limits are optimized together to minimize the expected cost per unit time, subject to a false‐alarm constraint. The framework estimates the false‐alarm and Type II error probabilities within the optimization using Monte Carlo simulation and bootstrap, which makes economic design feasible without closed‐form expressions. Numerical experiments cover several distributions and process scenarios, and the proposed schemes perform well in both statistical and economic terms. A case study on coating thickness data from lithium‐ion battery electrode manufacturing shows how the framework can be applied in practice.
ABSTRACT Reliability‐Based Design Optimization (RBDO) can require substantial computational effort because of repeated reliability evaluations and sensitivity calculations. This study investigates a Kriging‐assisted RBDO framework incorporating reverse‐mode automatic differentiation (AD). Original performance‐function evaluations provide training data, while AD is applied to the Kriging mean predictors to obtain sensitivities for Performance Measure Approach (PMA)‐based reliability analysis. The original black‐box model is not differentiated. Two analytical benchmark problems and a cantilever‐beam design problem are used to examine the framework. Relative to the classical RBDO implementation considered, the reported total constraint‐evaluation counts decrease by approximately 96% and 73% for the first two benchmark problems, respectively, while the cantilever‐beam example satisfies the prescribed target reliability index. Overall, the results indicate the computational potential of combining Kriging surrogate modeling with AD‐based sensitivity evaluation within PMA‐based RBDO. The study therefore presents an AD–Kriging implementation for surrogate‐based RBDO and demonstrates its application on representative benchmark problems.
Unsupervised anomaly detection plays a crucial role in prognostics and health management. Industrial equipment predominantly operates in a normal state throughout its service life, rendering faults rare and the collection of sufficient fault samples impractical. This necessitates unsupervised approaches that establish normality boundaries based on normal data. We propose a denoising diffusion probabilistic model (DDPM)‐enhanced anomaly detection framework, which integrates data augmentation techniques based on the DDPM, efficient dimensionality reduction via principal component analysis, and anomaly detection using the Isolation Forest algorithm. The proposed framework is applied to the CWRU and MFPT datasets, and the results demonstrate robust cross‐dataset consistency, with the AUC‐ROC differing by only 0.32 percentage points between the two datasets. Extensive comparative experiments show that DDPM outperforms the variational autoencoder (VAE) in data augmentation, achieving superior interclass separation (8.09σ vs. 5.70σ). Furthermore, early fault detection experiments reveal that under 10% fault signal contamination, DDPM‐based augmentation achieves 82% recall compared to 60% for VAE‐based augmentation. These results indicate that the proposed DDPM framework is effective for industrial condition monitoring, enabling efficient dimensionality reduction without compromising detection accuracy.
This article is a sequel to the previous by Maghsoodloo and Silva, where the authors derived the sampling distribution of log e ( S ) from the normal universe N( μ , 1). Our first objective is to generalize to the sampling distribution of y = log e ( S ), where the variate S represents the standard deviation of a random sample of size n ≥ 2 from a normal universe of any standard deviation σ > 0. We will then obtain the exact expressions for the first 4 moments of Ln( S | σ > 0), and the tabulations of the exact first 4 moments are provided in Tables 1 and 2; Table 1 values are then verified by Taylor's approximation; Table 3 compares the exact values of E[log e ( S )] versus those from the Taylor expansion.
