Bridging the gap between theory and practice in basic statistical process monitoring

ABSTRACT

Some issues are discussed relative to the gap between theory and practice in the area of statistical process monitoring (SPM). Among other issues, it is argued that the collection and use of baseline data in Phase I needs a greater emphasis. Also, the use of sample ranges in practice to estimate process standard deviations deserves reconsideration. A discussion is given on the role of modeling in SPM. Then some work on profile monitoring and the effect of estimation error on Phase II chart performance is summarized. Finally, some ways that researchers could influence practice more effectively are discussed along with how SPM research could become more useful to practitioners.     

Multivariate statistical process control charts: an overview

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart‐type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial least squares (PLS). Finally, we describe the most significant methods for the interpretation of an out‐of‐control signal. Copyright © 2006 John Wiley & Sons, Ltd.     

Statistical transfer learning: A review and some extensions to statistical process control

ABSTRACT

The rapid development of information technology, together with advances in sensory and data acquisition techniques, has led to the increasing necessity of handling datasets from multiple domains. In recent years, transfer learning has emerged as an effective framework for tackling related tasks in target domains by transferring previously-acquired knowledge from source domains. Statistical models and methodologies are widely involved in transfer learning and play a critical role, which, however, has not been emphasized in most surveys of transfer learning. In this article, we conduct a comprehensive literature review on statistical transfer learning, i.e., transfer learning techniques with a focus on statistical models and statistical methodologies, demonstrating how statistics can be used in transfer learning. In addition, we highlight opportunities for the use of statistical transfer learning to improve statistical process control and quality control. Several potential future issues in statistical transfer learning are discussed.     

Design of EWMA and CUSUM control charts subject to random shift sizes and quality impacts

Statistical process control charts are important tools for detecting process shifts. To ensure accurate, responsive fault detection, control chart design is critical. In the literature, control charts are typically designed by minimizing the control chart's responding time, i.e., average run length (ARL), to an anticipated shift size under a tolerable false alarm rate. However, process shifts, originating from various variation sources, often come with different sizes and result in different degrees of quality impacts. In this paper, we propose a new performance measure for EWMA and CUSUM control chart design to take into consideration the variable shift sizes and corresponding quality impacts. Unlike economic designs of control charts that suffer from a complex cost structure and intensive numerical computation, the proposed design methodology does not involve any cost estimation and the design procedure is as simple as looking up tables. Given the Gaussian random shifts and quadratic quality loss function, we show that the proposed design has a significant reduction in the quality impact as compared to conventional ARL-based designs. Guidelines and useful worksheets for practical implementation of the proposed designs are then suggested to practitioners with different knowledge levels of the process excursions.     

Dynamic probability control limits for CUSUM charts for monitoring proportions with time-varying sample sizes

We consider the problem of monitoring a proportion with time-varying sample sizes. Control charts are generally designed by assuming a fixed sample size or a priori knowledge of a sample size probability distribution. Sometimes, it is not possible to know, or accurately estimate, a sample size distribution or the distribution may change over time. An improper assumption for the sample size distribution could lead to undesirable performance of the control chart. To handle this problem, we propose the use of dynamic probability control limits (DPCLs) which are determined successively as the sample sizes become known. The method is based on keeping the conditional probability of a false alarm at a predetermined level given that there has not been any earlier false alarm. The control limits dynamically change, and the in-control performance of the chart can be controlled at the desired level for any sequence of sample sizes. The simulation results support this result showing that there is no need for any assumption of a sample size distribution with the use of this proposed approach.     

Monitoring acute and chronic kidney failure using statistical process control techniques

Creatinine tests are used to determine a patient's estimated glomerular filtration rate (eGFR) for the assessment of kidney function. This article describes how eGFR results for patients who need to have their cases referred for the attention of a specialist can be filtered out from among the numerous patients whose test results indicate that they are either displaying no reduction in kidney function or whose kidney function is reduced but remains stable. Automation of the process is a key ingredient of our solution because this is the means by which the human effort is directed to those patients in greatest need.     

Cluster-based artificial contrasts for inhomogeneously distributed data with an indicator variable

Multivariate statistical process control is used for simultaneously monitoring several process variables. The original artificial contrasts (AC) are very useful for monitoring inhomogeneously distributed data with an indicator variable. The cluster-based AC improve it by considering separated clusters, respectively. Then the artificial data used for the AC overlap each cluster. Numerical experiments show that our method outperforms existing methods in terms of Type-II error rate.     

Optimal EWMA of linear combination of Poisson variables for multivariate statistical process control

In this paper, we propose a new process control chart for monitoring correlated Poisson variables, the EWMA LCP chart. This chart is the exponentially weighted moving average (EWMA) version of the recently proposed LCP chart. The latter is a Shewhart-type control chart whose control statistic is a linear combination of the values of the different Poisson variables (elements of the Poisson vector) at each sampling time. As a Shewhart chart, it is effective at signalling large process shifts but is slow to signal smaller shifts. EWMA charts are known to be more sensitive to small and moderate shifts than their Shewhart-type counterparts, so the motivation of the present development is to enhance the performance of the LCP chart by the incorporation of the EWMA procedure to it. To ease the design of the EWMA LCP chart for the end user, we developed a user-friendly programme that runs on Windows© and finds the optimal design of the chart, that is, the coefficients of the linear combination as well as the EWMA smoothing constant and chart control limits that together minimise the out-of-control ARL under a constraint on the in-control ARL. The optimization is carried out by genetic algorithms where the ARLs are calculated through a Markov chain model. We used this programme to evaluate the performance of the new chart. As expected, the incorporation of the EWMA scheme greatly improves the performance of the LCP chart.     

Integrating artificial intelligence into on‐line statistical process control

Statistical process control (SPC) is one of the most effective tools of total quality management, the main function of which is to monitor and minimize process variations. Typically, SPC applications involve three major tasks in sequence: (1) monitoring the process, (2) diagnosing the deviated process and (3) taking corrective action. With the movement towards a computer integrated manufacturing environment, computer based applications need to be developed to implement the various SPC tasks automatically. However, the pertinent literature shows that nearly all the researches in this field have only focussed on the automation of monitoring the process. The remaining two tasks still need to be carried out by quality practitioners. This project aims to apply a hybrid artificial intelligence technique in building a real time SPC system, in which an artificial neural network based control chart monitoring sub‐system and an expert system based control chart alarm interpretation sub‐system are integrated for automatically implementing the SPC tasks comprehensively. This system was designed to provide the quality practitioner with three kinds of information related to the current status of the process: (1) status of the process (in‐control or out‐of‐control). If out‐of‐control, an alarm will be signaled, (2) plausible causes for the out‐of‐control situation and (3) effective actions against the out‐of‐control situation. An example is provided to demonstrate that hybrid intelligence can be usefully applied for solving the problems in a real time SPC system. Copyright © 2003 John Wiley & Sons, Ltd.     

Detection of pneumonia in chest X‐ray images by using 2D discrete wavelet feature extraction with random forest

Pneumonia is one of the most common and fatal diseases in the world. Early diagnosis and treatment are important factors in reducing mortality caused by the aforementioned disease. One of the most important and common techniques to diagnose pneumonia disease is the X‐ray images. By evaluating these images, various machine‐learning methods are used for accuracy in diagnosis. The presented study in this article utilizes machine‐learning techniques to evaluate these X‐ray images. The diagnosis of pediatric pneumonia is classified with a proposed machine learning method by using the chest X‐ray images. The proposed system firstly utilizes a two‐dimensional discrete wavelet transform to extract features from images. The features obtained from the wavelet method are labeled as normal and pneumonia and applied to the classifier for classification. Besides, Random Forest algorithm is used for the classification technique of 5856 X‐ray images. A 10‐fold cross‐validation method is used to evaluate the success of the proposed method and to ensure that the system avoided overfitting. By using various machine learning algorithms, simulation results reveal that the Random Forest method is proposed and it gives successful results. Results also show that, at the end of the training and validation process, the proposed method achieves higher success with an accuracy of 97.11%.     

Optimum variable-dimension EWMA chart for multivariate statistical process control

The variable-dimension T² control chart (VDT² chart) was recently proposed for monitoring the mean of multivariate processes in which some of the quality variables are easy and inexpensive to measure while other variables require substantially more effort or expense. The chart requires most of the times that only the inexpensive variables be sampled, switching to sampling all the variables only when a warning is triggered. It has good ARL performance compared with the standard T² chart, while significantly reducing the sampling cost. However, like the T² chart, it has limited sensitivity to small and moderate mean shifts. To detect such shifts faster, we developed an exponentially weighted moving average (EWMA) version of the VDT² chart, along with Markov chain models for ARL calculation, and software (made available) for optimizing the chart design. The optimization software, which is based on genetic algorithms, runs in Windows^© and has a friendly user interface. The performance analysis shows the great gain in performance achieved by the incorporation of the EWMA procedure.     

Multiple Attribute Control Charts with False Discovery Rate Control

The statistical cumulative sum (CUSUM) chart is a powerful tool for monitoring the attribute quality variable in manufacturing industry. In this article, we studied the multiplicity problem caused by simultaneously monitoring more than one attribute quality variable. Multiple binomial and Poisson CUSUM charts incorporating a multiple hypothesis testing technique known as false discovery rate control were proposed. The procedures for establishing the new control schemes were presented, and the performance of the new methods was evaluated using Monte Carlo simulation. The approximation methods for obtaining the p‐values of the CUSUM statistics for conducting the new control schemes were also provided and evaluated. The new methods were also illustrated with a real example. Copyright © 2011 John Wiley & Sons, Ltd.     

Comparisons of Shewhart-type rank based control charts for monitoring location parameters of univariate processes

The nonparametric (distribution-free) control charts are robust alternatives to the conventional parametric control charts when the form of underlying process distribution is unknown or complicated. In this paper, we consider two new nonparametric control charts based on the Hogg–Fisher–Randle (HFR) statistic and the Savage rank statistic. These are popular statistics for testing location shifts, especially in right-skewed densities. Nevertheless, the control charts based on these statistics are not studied in quality control literature. In the current context, we study phase-II Shewhart-type charts based on the HFR and Savage statistics. We compare these charts with the Wilcoxon rank-sum chart in terms of false alarm rate, out-of-control average run-length and other run length properties. Implementation procedures and some illustrations of these charts are also provided. Numerical results based on Monte Carlo analysis show that the new charts are superior to the Wilcoxon rank-sum chart for a class of non-normal distributions in detecting location shift. New charts also provide better control over false alarm when reference sample size is small.     

Approximate design and performance of the robust control charts for monitoring dispersion in Phase I

This article designs and studies the approximate performance of robust dispersion charts, namely, MAD chart, S_n chart, and Q_n chart, in Phase I analysis (recently developed in the literature). The proposed limits are based on false alarm probability for monitoring the dispersion of a process in Phase I analysis. The charting constants are determined to achieve the required nominal FAP (FAP₀). The performance of these structures is evaluated in (i) the attained false alarm rate and (ii) the probability of signals for out‐of‐control situations. The analysis shows that the proposed design of Phase I robust dispersion charts correctly controls the FAP and shows a good performance in detecting the shifts in the process variation. An illustrative example is used to explain the practical implementation of these limits.     

Decision tree based control chart pattern recognition

This paper presents a new approach to classify six anomaly types of control chart patterns (CCP), of systematic pattern, cyclic pattern, upward shift, downward shift, upward trend, and downward trend. Current CCP recognition methods use either unprocessed raw data or complex transformed features (via principal component analysis or discrete wavelet transform) as the input representation for the classifier. The objective of using selected features is not only for dimension reduction of input representation, but also implies the process of data compression. In contrast, using raw data is often computationally inefficient while using transformed features is very tedious in most cases. Therefore, owing to its computational advantage, using appropriate features of CCP to achieve good classification accuracy becomes more promising in real process implementation. In this study, using three features of CCP shows quite a competitive performance in terms of classification accuracy and computational loading. More importantly, the proposed method presented here has potential to be generalized to medical, financial, and other application of temporal data.     

Monitoring a fraction with easy and reliable settings of the false alarm rate

Monitoring a fraction arises in many manufacturing applications and also in service applications. The traditional p‐chart is easy to use and design but is difficult to achieve the desired false alarm rate. We propose a two‐sided CUSUM Arcsine method that achieves both large and small desired false alarm rates for an in‐control probability anywhere between 0 and 1. The parameters of the new method are calculated easily, without tables, simulation, or Markov chain analysis used by many of the existing methods. The proposed method detects increases and decreases and works for constant and Poisson distributed sample sizes. The CUSUM Arcsine also has a superior sensitivity compared with other easily designed existing methods for monitoring Binomial distributed data. This paper includes an extensive literature review and a taxonomy of the existing monitoring methods for a fraction. Copyright © 2009 John Wiley & Sons, Ltd.     

Integrating statistical process monitoring with feedforward control

Feedforward control is a particular form of engineering process control. If a known input variable z_t can be measured and appropriate relationships built between the input variable, a compensatory variable x_t, and the desired output y_t, then a feedforward control system can be developed. Using feedforward control, we show under both sudden jump shifts and trends in the mean of the input and compensatory variables that the use of statistical process monitoring tools, such as the exponentially‐weighted moving average and the cumulative sum (CUSUM), significantly reduces variability in both the output variable and the controller relative to the use of feedforward control alone. Copyright © 2000 John Wiley & Sons, Ltd.     

Short-run statistical process control: Q-chart enhancements and alternative methods

In processes where the length of the production run is short, data to estimate the process parameters and control limits may not be available prior to the start of production, and because of the short run time, traditional methods for establishing control charts cannot be easily applied. Recently, Q charts have been proposed to address this problem. We study the average run length (ARL) of Q charts for a normally distributed variable assuming that a sustained shift occurs in the quality characteristic. It is shown that in some cases Q charts do not exhibit adequate ARL performance. Modifications that enhance the ARL properties of Q charts are presented. Some alternatives to Q charts are also discussed. For the case of a known process target two alternative methods are presented: an exponentially weighted moving average (EWMA) method and an adaptive Kalman filtering method. It is shown that both methods have better ARL performance than Q charts for that case. For the case of both process parameters unknown, an adaptive Kalman filtering method used with a tracking signal provides an ARL performance that improves as better estimates of the process mean and variance are given. A practical example illustrates the tracking signal method for the case when the process parameters are unknown.     

Integrated production,statistical process control,and maintenance policy for unreliable manufacturing systems

The objective of this paper is to develop an integrated approach for the joint control of production, maintenance and quality for batch manufacturing systems. We consider such systems that are subject to degradation which is at the origin of the production of defective units. The quality control of lots produced is performed using an ‘x-bar’ control chart. This graphical tool will allow estimating the quality of the batch being produced and possibly undertake perfect preventive or corrective maintenance actions on the production system. A buffer stock is built to maintain continuity of supply during maintenance actions. The incurred total cost includes setup cost, inventory costs, the cost of unused products, maintenance costs and quality costs. Decision variables include the buffer stock size, the sample size, the sampling interval, the surveillance and the control limits of the control chart. Numerical experiments and sensitivity analyses are provided to evaluate the effectiveness of the proposed control policy and the robustness of the solving approach.     

On efficient construction and evaluation of runs rules–based control chart for known and unknown parameters under different distributions

In this study, we have considered two design structures of control chart by covering the situations of known and unknown parameters, variety of probability distributions, and runs rules. The design structures are dependent on constants which generally considered hard to compute analytically. For construction of constants and also for evaluating performance of the design structures through performance measures, we have illustrated Monte Carlo simulation procedure/algorithm for researcher and practitioners. Furthermore, based on the Monte Carlo simulation procedures, we have established a program in R language to compute values of different constants and performance measures. Results illustrated that design structures for known and unknown parameters under variety of runs rules and probability distributions have outstanding performance in contrast to existing structures. Moreover, design structure for unknown parameters behaves alike the design structure for known parameters. This indicates that design structure for unknown parameters has the ability to resolve the issue of runs rules which generally occur when parameters are estimated. Besides, two real‐life examples have been included in which physicochemical characteristic of groundwater and plasticizer characteristic of petrochemical process are monitored through design structures.