A phase I multi-modelling approach for profile monitoring of signal data

Many industrial processes exhibit multiple in-control signatures, where signal data vary over time without affecting the final product quality. They are known as multimode processes. With regard to profile monitoring methodologies, the existence of multiple in-control patterns entails the study and development of novel monitoring schemes. We propose a method based on coupling curve classification and monitoring that inherits the so-called ‘multi-modelling framework’. The goal is to design a monitoring tool that is able to automatically adapt the control chart parameters to the current operating mode. The proposed approach allows assessing which mode new data belong to before applying a control chart to determine if they are actually in control or not. Contrary to mainstream multi-modelling techniques, we propose extending the classification step to include a novelty detection capability, in order to deal with the possible occurrence of in-control operating modes during the design phase that were not observed previously. The functional data depth paradigm is proposed to design both the curve classification and the novelty detection algorithm. A simulation study is presented to demonstrate the performances of the proposed methodology, which is compared against benchmark methods. A real case study is presented too, which consists of a multimode end-milling process, where different operating conditions yield different cutting force profile patterns.     

A multivariate CUSUM control chart for monitoring Gumbel's bivariate exponential data

Exponentially distributed data are commonly encountered in high-quality processes. Control charts dedicated to the univariate exponential distribution have been extensively studied by many researchers. In this paper, we investigate a multivariate cumulative sum (MCUSUM) control chart for monitoring Gumbel's bivariate exponential (GBE) data. Some tables are provided to determine the optimal design parameters of the proposed MCUSUM GBE chart. Furthermore, both zero-state and steady-state properties of the proposed MCUSUM GBE chart for the raw and the transformed GBE data are compared with the multivariate exponentially weighted moving average (MEWMA) chart and the paired individual cumulative sum (CUSUM) chart. The results show that the proposed MCUSUM GBE chart outperforms the other two types of control charts for most shift domains. In addition, an extension to Gumbel's multivariate exponential (GME) distribution is also investigated. Finally, an illustrative example is provided in order to explain how the proposed MCUSUM GBE chart can be implemented in practice.     

A comparison study of control charts for statistical monitoring of functional data

The quality of products and processes is more and more often becoming related to functional data, which refer to information summarised in the form of profiles. The recent literature has pointed out that traditional control charting methods cannot be directly applied in these cases and new approaches for profile monitoring are required. While many different profile monitoring approaches have been proposed in the scientific literature, few comparison studies are available. This paper aims at filling this gap by comparing three representative profile monitoring approaches in different production scenarios. The performance comparison will allow us to select a specific approach in a given situation. The competitor approaches are chosen to represent different levels of complexity, as well as different types of modelling approaches. In particular, at a lower level of complexity, the ‘location control chart’ (where the upper and lower control limits are ±K standard deviations from the sample mean at each profile location) is considered to be representative of industrial practice. At a higher complexity level, approaches based on combining a parametric model of functional data with multivariate and univariate control charting are considered. Within this second class, we analyse two different approaches. The first is based on regression and the second focuses on using principal component analysis for modelling functional data. A manufacturing reference case study is used throughout the paper, namely profiles measured on machined items subject to geometrical specification (roundness).     

A spatial variable selection method for monitoring product surface

Two-dimensional (2-D) data maps are generated in certain advanced manufacturing processes. Such maps contain rich information about process variation and product quality status. As a proven effective quality control technique, statistical process control (SPC) has been widely used in different processes for shift detection and assignable cause identification. However, charting algorithms for 2-D data maps are still vacant. This paper proposes a variable selection-based SPC method for monitoring 2-D wafer surface. The fused LASSO algorithm is firstly employed to identify potentially shifted sites on the surface; a charting statistic is then developed to detect statistically significant shifts. As the variable selection algorithm can nicely preserve shift patterns in spatial clusters, the newly proposed chart is proved to be both effective in detecting shifts and capable of providing diagnostic information for process improvement. Extensive Monte Carlo simulations and a real example have been used to demonstrate the effectiveness and usage of the proposed method.     

A tensor-based hierarchical process monitoring approach for anomaly detection in additive manufacturing

Additive manufacturing (AM) is a technology that enables the creation of complex shapes with advanced structural and functional properties. It has transformed the traditional manufacturing operations into a more flexible and efficient process, reshaping the whole value chain and allowing new levels of product customization. AM is a layer-by-layer manufacturing process, in which materials are deposited in each layer to create the object of interest. Due to the layer-wise nature of the process, anomalies and defects might occur within each layer, across several layers or throughout the whole sample. An accurate and responsive detection strategy that enables the detection of various types of anomalies is essential for ensuring the quality and integrity of the manufactured product. In this paper, a hierarchical in situ process monitoring approach, namely, a three level monitoring strategy, is proposed to detect local, layer-wise, and sample-wise anomalies using thermal videos acquired during the manufacturing process. The proposed approach integrates hierarchical low-rank tensor decomposition methods with statistical monitoring techniques to effectively detect anomalies at different levels, namely, the within-layer level, the layer level, and the sample level. Simulations are used to evaluate the performance of the method and compare with existing benchmarks. The proposed approach is also applied to thermal videos acquired during the laser powder bed fusion (L-PBF) process to illustrate its effectiveness in practice.     

Adaptive CUSUM and EWMA charts with auxiliary information and variable sampling intervals for monitoring the process mean

The variable sampling interval (VSI) feature enhances the sensitivity of a control chart that is based on fixed sampling interval (FSI). In this paper, we enhance the sensitivities of the auxiliary information-based (AIB) adaptive Crosier cumulative sum (CUSUM) (AIB-ACC) and adaptive exponentially weighted moving average (EWMA) (AIB-AE) charts using the VSI feature when monitoring a mean shift which is expected to lie within a given interval. The Monte Carlo simulations are used to compute zero-state and steady-state run length properties of these control charts. It is found that the AIB-ACC and AIB-AE charts with VSI feature are uniformly more sensitive than those based on FSI feature. Real datasets are also considered to demonstrate the implementation of these control charts.     

Multilevel spatial randomness approach for monitoring changes in 3D topographic surfaces

The 3D surface topography of finished products is a key characteristic for monitoring the quality of products and manufacturing processes. The topography has unique properties in which the topographic values are spatially autocorrelated with their neighbours and the locations of topographic values randomly change from one surface to another under the in-control process behaviour, making the online detection of local topographic changes challenging. Due to the complex structure of topographic data, the existing monitoring approaches lack the detection of local changes. Therefore, we develop a novel online monitoring approach for detecting local changes in 3D topographic surfaces. We introduce a multilevel surface thresholding algorithm for enhancing the representation of topographic values by slicing the 3D surface topography into cumulative levels in reference to the characteristics of the in-control surfaces. The spatial and random properties of topographic values are quantified at each surface level through the proposed spatial randomness profile. After obtaining the spatial randomness profile, an effective monitoring statistic based on the functional principal component analysis is developed for detecting anomaly surfaces. The proposed approach shows superior performance in identifying a wide range of fault patterns and outperforms the existing approaches in both simulated and real-life topographic data.     

Functional Process Capability Indices for Circular Profile

Profile is a relation between one response variable and one or more explanatory variables that represent quality of a product or performance of a process. On the other hand, process capability indices are measures to help practitioners in improving the processes to satisfy the customer's expectations. Few researches are done to account for the process capability index in the areas of profile monitoring. All of these researches are focused on process capability index in simple linear profile. In all of these methods, response variables in different levels of explanatory variable are considered, and the relationship in all range of explanatory variable is neglected. In this paper, a functional method is proposed to measure process capability index of circular profiles in all range of explanatory variable. The proposed method follows the traditional definition of process capability indices. The functional method uses reference profile, functional specification limits and functional natural tolerance limits to present a functional form of process capability indices. This functional form results in measuring the process capability in each level of explanatory variable in circular profile as well as a unique value of process capability index for circular profile. The application of the proposed method is illustrated through a real case in automotive industry. Copyright © 2013 John Wiley & Sons, Ltd.     

Using economically designed Shewhart and adaptive ―X charts for monitoring the quality of tiles

This paper presents the economic design of ―X control charts for monitoring a critical stage of the main production process at a tile manufacturer in Greece. Two types of ―X charts were developed: a Shewhart‐type chart with fixed parameters and adaptive charts with variable sampling intervals and/or sample size. Our prime motivation was to improve the statistical control scheme employed for monitoring an important quality characteristic of the process with the objective of minimizing the relevant costs. At the same time we tested and confirmed the applicability of the theoretical models supporting the economic design of control charts with fixed and variable parameters in a practical situation. We also evaluated the economic benefits of moving from the broadly used static charts to the application of the more flexible and effective adaptive control charts. The main result of our study is that, by redesigning the currently employed Shewhart chart using economic criteria, the quality‐related cost is expected to decrease by approximately 50% without increasing the implementation complexity. Monitoring the process by means of an adaptive ―X chart with variable sampling intervals will increase the expected cost savings by about 10% compared with the economically designed Shewhart chart at the expense of some implementation difficulty. Copyright © 2006 John Wiley & Sons, Ltd.     

Statistical process monitoring of time-dependent data

ABSTRACT

During the last decades, we evolved from measuring few process variables at sparse intervals to a situation in which a multitude of variables are measured at high speed. This evidently provides opportunities for extracting more information from processes and to pinpoint out-of-control situations, but transforming the large data streams into valuable information is still a challenging task. In this contribution we will focus on the analysis of time-dependent processes since this is the scenario most often encountered in practice, due to high sampling systems and the natural behavior of many real-life applications. The modeling and monitoring challenges that statistical process monitoring (SPM) techniques face in this situation will be described and possible routes will be provided. Simulation results as well as a real-life data set will be used throughout the article.     

Modeling and monitoring the nonlinear profile of heat treatment process data by using an approach based on a hyperbolic tangent function

In this article, a new approach is proposed which uses the hyperbolic tangent function to model and monitor vacuum heat treatment process data. The proposed hyperbolic tangent function approach is compared to the smoothing spline approach. The latter serves as the benchmark when the vacuum heat treatment profile is investigated. The vector of the obtained parameter estimates is monitored by using Hotelling's method for the hyperbolic tangent function approach, and the metrics method used for the smoothing spline approach. For the purposes of verification, data from a real aluminum alloy heat treatment process is used to illustrate the proposed approach. In Phase I, the modified hyperbolic tangent function and the smoothing spline are first utilized to fit the process data. The proposed approach provides a better fitting result than the smoothing spline approach. In Phase II, the proposed approach produces a much better out-of-control average run length (ARL) performance than the smoothing spline approach when the heat treatment profile shows process abnormalities.     

A Bayesian approach to sequential monitoring of nonlinear profiles using wavelets

We consider change‐point detection and estimation in sequences of functional observations. This setting often arises when the quality of a process is characterized by such observations, called profiles, and monitoring profiles for changes in structure can be used to ensure the stability of the process over time. While interest in phase II profile monitoring has grown, few methods approach the problem from a Bayesian perspective. We propose a wavelet‐based Bayesian methodology that bases inference on the posterior distribution of the change point without placing restrictive assumptions on the form of profiles. By obtaining an analytic form of this posterior distribution, we allow the proposed method to run online without using Markov chain Monte Carlo (MCMC) approximation. Wavelets, an effective tool for estimating nonlinear signals from noise‐contaminated observations, enable us to flexibly distinguish between sustained changes in profiles and the inherent variability of the process. We analyze observed profiles in the wavelet domain and consider two possible prior distributions for coefficients corresponding to the unknown change in the sequence. These priors, previously applied in the nonparametric regression setting, yield tuning‐free choices of hyperparameters. We present additional considerations for controlling computational complexity over time and their effects on performance. The proposed method significantly outperforms a relevant frequentist competitor on simulated data.     

Efficient global monitoring statistics for high-dimensional data

Global monitoring statistics play an important role in developing efficient monitoring schemes for high-dimensional data. A number of global monitoring statistics have been proposed in the literature. However, most of them only work for certain types of abnormal scenarios under specific model assumptions. How to develop global monitoring statistics that are powerful for any abnormal scenarios under flexible model assumptions is a long-standing problem in the statistical process monitoring field. To provide a potential solution to this problem, we propose a novel class of global monitoring statistics. Our proposed global monitoring statistics are easy to calculate and can work under flexible model assumptions since they can be built on any local monitoring statistic that is suitable for monitoring a single data stream. Our simulation studies show that the proposed global monitoring statistics perform well across a broad range of settings and compare favorably with existing methods.     

Statistical process monitoring via image data using wavelets

Image data plays an important role in manufacturing and service industries because each image can provide a huge set of data points in just few seconds with relatively low cost. Enhancement of machine vision systems during the time has led to higher quality images, and the use of statistical methods can help to analyze the data extracted from such images efficiently. It is not efficient from time and cost point of views to use every single pixel in an image to monitor a process or product performance effectively. In recent years, some methods are proposed to deal with image data. These methods are mainly applied for separation of nonconforming items from conforming ones, and they are rarely applied to monitor process capability or performance. In this paper, a nonparametric regression method using wavelet basis function is developed to extract features from gray scale image data. The extracted features are monitored over time to detect process out‐of‐control conditions using a generalized likelihood ratio control chart. The proposed approach can also be applied to find change point and fault location simultaneously. Several numerical examples are used to evaluate performance of the proposed method. Results indicate suitable performance of the proposed method in detecting out‐of‐control conditions and providing precise diagnostic information. Results also illustrate suitable performance of our proposed method in comparison with a competitive approach.     

Phase I monitoring of social networks based on Poisson regression profiles

Nowadays, due to the increasing role of social networks in our daily life, monitoring and forecasting social trends have attracted the attention of many researchers. To the best of the authors' knowledge, the literature includes few studies of monitoring social networks. Existing researches have focused on analyzing only the existence of communications between people and have neglected to monitor the number of such communications. In this paper, first counts of communications between people are modeled using Poisson regression profiles. Then, 3 Phase I monitoring methods, extended T², F, and a standardized likelihood ratio test method is suggested to detect step changes, drift, and outliers in the parameters of Poisson regression profiles. The proposed methods are evaluated via simulation studies in terms of signal probability criterion. The results show that in most out‐of‐control situations the standardized likelihood ratio test method outperforms the T² and F methods. Then, a numerical example and a case study based on Enron email data are presented to illustrate the application of the extended methods.     

基于密度的轮廓控制参数识别方法研究

正确识别受控轮廓集并确定轮廓控制参数是轮廓控制的基础。当轮廓内部存在相关关系时,异常轮廓对目前轮廓控制参数识别方法的干扰较大。因此,为降低异常轮廓对轮廓控制参数识别方法的影响,提出一种基于密度的受控轮廓集识别方法。该方法包括基于线性混合模型的轮廓建模、基于密度的初始受控轮廓集确定、基于逐次迭代方法的受控轮廓集识别和轮廓控制参数确定等。基于蒙特卡洛模拟分析所提方法中初始受控轮廓数目和密度参数对识别性能的影响。此外,比较分析所提方法与已有方法的识别性能。模拟仿真显示,基于密度的轮廓控制参数识别方法的识别性能要优于其他方法。     

A Cumulative Sum scheme for monitoring frequency and size of an event

This article proposes a Cumulative Sum (CUSUM) scheme, called the TC‐CUSUM scheme, for monitoring a negative or hazardous event. This scheme is developed using a two‐dimensional Markov model. It is able to check both the time interval (T) between occurrences of the event and the size (C) of each occurrence. For example, a traffic accident may be defined as an event, and the number of injured victims in each case is the event size. Our studies show that the TC‐CUSUM scheme is several times more effective than many existing charts for event monitoring, so that cost or loss incurred by an event can be reduced by using this scheme. Moreover, the TC‐CUSUM scheme performs more uniformly than other charts for detecting both T shift and C shift, as well as the joint shift in T and C. The improvement in the performance is achieved because of the use of the CUSUM feature and the simultaneous monitoring of T and C. The TC‐CUSUM scheme can be applied in manufacturing systems, and especially in non‐manufacturing sectors (e.g. supply chain management, health‐care industry, disaster management, and security control). Copyright © 2009 John Wiley & Sons, Ltd.     

LRProb control chart based on logistic regression for monitoring mean shifts of auto-correlated manufacturing processes

With the growth of automation in manufacturing, process quality characteristics are being measured at higher rates and data is more likely to be auto-correlated. Traditional statistical process control (SPC) techniques of control charting are not applicable in many process industries because process parameters are highly auto-correlated. Several attempts such as some time series based control charts have been made in the previous years to extend traditional SPC techniques. However, these extensions pose some serious limitations for monitoring the process mean shifts. These charts require that a suitable model has been identified for the time series of process observations before residuals can be obtained. In this paper, a logistic regression (LR)-based process monitoring model is proposed for enhancing the monitoring of processes. It is capable of providing a comprehensible and quantitative assessment value for the current process state, which is achieved by the event occurrence probability calculation of LR. Based on these probability values over the time series, a novel chart: LRProb chart, is developed for monitoring and visualising process changes. The aim of this research is to analyse the performance of the LRProb chart under the assumption that only a small number of predictable abnormal patterns are available. To such aim, the performance of the LRProb chart is evaluated on two real-world industrial cases and simulated processes. Given the simplicity, visualisation and quantification of the proposed LRProb chart, this approach is proved from the experiments to be a feasible alternative for quality monitoring in the case of auto-correlated process data.     

Statistical monitoring of nonlinear product and process quality profiles

In many quality control applications, use of a single (or several distinct) quality characteristic(s) is insufficient to characterize the quality of a produced item. In an increasing number of cases, a response curve (profile) is required. Such profiles can frequently be modeled using linear or nonlinear regression models. In recent research others have developed multivariate T² control charts and other methods for monitoring the coefficients in a simple linear regression model of a profile. However, little work has been done to address the monitoring of profiles that can be represented by a parametric nonlinear regression model. Here we extend the use of the T² control chart to monitor the coefficients resulting from a parametric nonlinear regression model fit to profile data. We give three general approaches to the formulation of the T² statistics and determination of the associated upper control limits for Phase I applications. We also consider the use of non‐parametric regression methods and the use of metrics to measure deviations from a baseline profile. These approaches are illustrated using the vertical board density profile data presented in Walker and Wright (Comparing curves using additive models. Journal of Quality Technology 2002; 34:118–129). Copyright © 2007 John Wiley & Sons, Ltd.