Both process monitoring and fault isolation are important and challenging tasks for quality control and improvement in high-dimensional processes. Under a practical assumption that not all variables would shift simultaneously, this paper proposes a variable-selection-based multivariate statistical process control (SPC) procedure for process monitoring and fault diagnosis. A forward-selection algorithm is first utilized to screen out potential out-of-control variables; a multivariate control chart is then set up to monitor suspicious variables. Therefore, detection of faulty conditions and isolation of faulty variables can be achieved in one step. Both simulation studies and a real example have shown the effectiveness of the proposed procedure.

Fault detection and root cause identification are both important tasks in Multivariate Statistical Process Control (MSPC) for improving process and product quality. Most traditional control charts, including Hotelling's T² chart and the Multivariate Exponential Weighted Moving Average (MEWMA) chart, separate the two tasks into independent and successive procedures by signaling the existence of process faults followed by auxiliary methods to locate root causes. This paper proposes an integrated procedure, a Variable-Selection-based MEWMA (VS-MEWMA) chart, for multivariate process monitoring and fault diagnosis by utilizing dimensionality reduction techniques. The VS-MEWMA chart first locates potentially out-of-control variables via variable selection and then deploys such information in the monitoring statistics with the reduction in dimensionality providing increased sensitivity to out-of-control conditions. When a signal is given, the algorithm also identifies the suspected variables for further root cause diagnosis. Both numerical simulations and real examples are presented to illustrate the performance of the proposed chart, as well as design guidelines.

In some manufacturing processes, the quality characteristic is represented by a two-dimensional (2-D) surface. Surface data can generally be treated as a special profile with one response variable and two explanatory variables, for which spatial correlations are commonly observed. Existing parametric charts for profile monitoring are unable to adequately describe the spatial correlations among variables in 2-D surface data, and nonparametric charts cannot be applied to a 2-D data structure directly. In this study, we propose a new chart based on the Gaussian-Kriging model, in which the spatial correlations within the 2-D surface profile are represented by a parametric function. We construct a parametric model that considers three components of the surface—the global trend, the spatial correlations, and independent errors. Then we monitor the process by detecting changes in the estimated parameters. We utilize this method to monitor a wafer-manufacturing process and compare its performance with that of an existing profile-monitoring method through simulation.

In many industrial multivariate quality control applications, based on the engineering and operational understanding of how the process works, when the process variability is out of control it is typically the case that changes only occur in a small number of elements in the covariance matrix. Under such a premise, we propose a new Phase II Shewhart chart for monitoring changes in the covariance matrix of a multivariate normal process. The new control chart is essentially based on calculating the likelihood ratio of testing the hypothesis that the in-control covariance matrix is equal to a known covariance matrix, where the unknown covariance matrix that appears in the likelihood ratio is replaced by an estimate obtained from a penalized likelihood function. The penalized likelihood function is derived by adding an L ₁ penalty function to the usual likelihood. The performance of the proposed chart is evaluated based on simulations and compared with that of several existing Shewhart charts for monitoring the covariance matrix. The simulation results indicate that the proposed chart outperforms existing charts. A real example from the semiconductor industry is presented and analyzed using the proposed chart and other existing charts. Potential future research directions are also discussed.

Nano-reliability measures the ability of a nano-scaled product to perform its intended functionality. At the nano scale, the physical, chemical, and biological properties of materials differ in fundamental, valuable ways from the properties of individual atoms, molecules, or bulk matter. Conventional reliability theories need to be restudied to be applied to nano-engineering. Research on nano-reliability is extremely important due to the fact that nano-structure components account for a high proportion of costs, and serve critical roles in newly designed products. This review introduces the concepts of reliability to nano-technology; and presents the current work on identifying various physical failure mechanisms of nano-structured materials, and devices during fabrication process, and operation. Modeling techniques of degradation, reliability functions, and failure rates of nano-systems are also reviewed in this work.