Many existing studies on profile monitoring focus on parametric profiles or normally distributed responses, and usually assume that the design points within different profiles are deterministic. In practice, however, profiles with count responses are common, and different profiles often have different within-profile sample sizes and design points. Furthermore, it is difficult to fit models to complex profiles with multiple explanatory variables either parametrically or nonparametrically. This article aims to monitor small-sample size profiles with count response and arbitrary design using a semiparametric model. Two novel control schemes with dynamic control limits are proposed based on the weighted likelihood ratio test and the weighted F test, respectively. Numerical simulations are conducted to investigate the performance of the proposed control charts. The performance between the control chart with constant and dynamic control limits is also compared, and the effect of model misspecification is explored. Finally, a real-data example of automobile warranty claims is presented to illustrate the implementation of the proposed control charts.

Semiparametric control schemes for dynamically monitoring profiles with count data and arbitrary design

In Statistical Process Control, profile monitoring is used for monitoring whether the process is in‐control or not by checking the relationship stability between the process response and covariates. In the industrial process recently, the functional relationship between the process variables is more and more complex, and the profile data are often time‐dependent and subject to within‐profile autocorrelation. We need to use appropriate models to characterize these complex relationships, and design new profile monitoring schemes to ensure satisfactory process monitoring performance. This paper studies a practical nonparametric profile monitoring problem, in which the functional relationship is in the form of function‐on‐scalar and within‐profile data are autocorrelated. A new online profile monitoring scheme is proposed to monitor process anomalies in real time. In Phase Ⅰ, based on the in‐control historical data, the model for the process is established estimated. Then, using the monitoring statistics based on penalty spline smoothing, the function‐on‐scalar monitoring parameters control scheme with a moving window is presented, and is applied to the anomaly monitoring of online sequential profile data. A large number of numerical simulation results show that in the presence of the function‐on‐scalar relationship, the proposed scheme has a superior performance in various cases. Finally, an application example of industrial busbar running process monitoring is given to illustrate the effectiveness of the scheme.

Online monitoring of profiles via function‐on‐scalar model with an application to industrial busbar

Calibration is the backbone of any sensor and measurement philosophy. The conventional calibration techniques for electrical parameter measurement using nonlinear sensors are affected by the repeating analogue signals and lead to errors in measurement. This research paper investigates different regression‐based mathematical models to calibrate the Hall sensor for measuring RMS and the fundamental frequency. The novelty of this research work lies in the feature‐based input modelling to measure RMS current and frequency with an error of 3.37e‐12% and 7.61e‐9%, respectively. The conventional Fourier transform method is compared with six different bio‐inspired metaheuristic algorithms to estimate the frequency components of the analogue signal received from the measurement setup. Apart from the conventional sine waveforms, this paper investigates sawtooth and square waveforms as the periodic signals for determining the frequency components. The results from the comparison study show that the Whale Optimization Algorithm exhibits 1.25% lesser error whilst predicting the features in measured frequency components. Apart from this, the paper identifies a unique combination of features that effectively measures the instantaneous electrical parameter with RMSE, NRMSE, and R2 value of 158.8, 0.51, and 0.44, respectively. Experimentally it is found that the decision tree and random forest regression models calibrate the Hall sensor with 93% less error than their linear and polynomial counterparts.

Calibration and frequency estimation in sensors for electrical parameter measurement using regression and metaheuristic based models

Control charts are often used to monitor the quality characteristics of a process over time to ensure undesirable behavior is quickly detected. The escalating complexity of processes we wish to monitor spurs the need for more ﬂexible control charts such as those used in proﬁle monitoring. Additionally, designing a control chart that has an acceptable false alarm rate for a practitioner is a common challenge. Alarm fatigue can occur if the sampling rate is high (say, once a millisecond) and the control chart is calibrated to an average in-control run length ( ARL 0 ) of 200 or 370 which is often done in the literature. As alarm fatigue may not just be an annoyance but result in detrimental effects to the quality of the product, control chart designers should seek to minimize the false alarm rate. Unfortunately, reducing the false alarm rate typically comes at the cost of detection delay or average out-of-control run length ( ARL 1 ). Motivated by recent work on eigenvector perturbation theory, we develop a computationally fast control chart called the Eigenvector Perturbation Control Chart for nonparametric proﬁle monitoring. The control chart monitors the l 2 perturbation of the leading eigenvector of a correlation matrix and requires only a sample of known in-control proﬁles to determine control limits. Through a simulation study we demonstrate that it is able to outperform its competition by achieving an ARL 1 close to or equal to 1 even when the control limits result in a large ARL 0 on the order of 10 6 . Additionally, non-zero false alarm rates with a change point after 10 4 in-control observations were only observed in scenarios that are either pathological or truly difﬁcult for a correlation based monitoring scheme.

Takayuki Iguchi

Papers

Nonlinear profile monitoring with single index models