Statistical Process Control Monitoring Research Articles

Design and properties of the predictive ratio cusum (PRC) control charts

In statistical process control/monitoring (SPC/M), memory-based control charts aim to detect small/medium persistent parameter shifts. When a phase I calibration is not feasible, self-starting methods have been proposed, with the predictive ratio cusum (PRC) being one of them. To apply such methods in practice, one needs to derive the decision limit threshold that will guarantee a preset false alarm tolerance, a very difficult task when the process parameters are unknown and their estimate is sequentially updated. Utilizing the Bayesian framework in PRC, we will provide the theoretic framework that will allow to derive a decision-making threshold, based on false alarm tolerance, which along with the PRC closed-form monitoring scheme will permit its straightforward application in real-life practice. An enhancement of PRC is proposed, and a simulation study evaluates its robustness against competitors for various model type misspecifications. Finally, three real data sets (normal, Poisson, and binomial) illustrate its implementation in practice. Technical details, algorithms, and R-codes reproducing the illustrations are provided as supplementary material.

Effect of contaminated phase I data on the phase II – EWMA control chart performance under non-normality

Estimation of unknown process parameters is critical in statistical process control/monitoring (SPC/M). Retrospective data is usually used to identify the process in-control state behavior in terms of estimating the process parameters. Practitioners analyze the retrospective data in order to handle out-of-control observations before estimating the parameters. However, chances to overlook some out-of-control observations do exist; in which case, the Phase I data is said to be contaminated. In this study, we aim to assess the impact of having contaminated retrospective data on the performance of the EWMA chart; assuming non-normal processes. Two distributions are considered; the t-distribution to represent a symmetric heavy-tailed distribution with two contamination scenarios, and the Gamma distribution to represent a skewed one. A weighted variance EWMA chart is used with the Gamma distribution to account for the skewness. Our results revealed that under the t-distribution a contamination with respect to the mean is more serious than a contamination with respect to the degrees of freedom. Under the gamma distribution, the estimation effect generally and contamination effect specifically are more serious on smaller shape parameter values (heavily skewed).

Application of statistical process control for spotting compliance to good pharmaceutical practice

For the release of pharmaceutical products into the drug market; most of the pharmaceutical companies depend on acceptance criteria - that are set internally, regulatory and/or pharmacopeially. However, statistical process control monitoring is underestimated in most quality control in cases; although it is important not only for process stability and efficiency assessment but also for compliance with all appropriate pharmaceutical practices such as good manufacturing practice and good laboratory practice, known collectively as GXP. The current work aims to investigate two tablet inspection characteristics monitored during in-process control viz. tablet average weight and hardness. Both properties were assessed during the compression phase of the tablet and before the coating stage. Data gathering was performed by the Quality Assurance Team and processed by Commercial Statistical Software packages. Screening of collected results of 31 batches of an antibacterial tablet - based on Fluoroquinolone -showed that all the tested lots met the release specifications, although the process mean has been unstable which could be strongly evident in the variable control chart. Accordingly, the two inspected processes were not in the state of control and require strong actions to correct for the non-compliance to GXP. What is not controlled cannot be predicted in the future and thus the capability analysis would be of no value except to show the process capability retrospectively only. Setting the rules for the application of Statistical Process Control (SPC) should be mandated by Regulatory Agencies.

Design Performance Analysis of a Self-Organizing Map for Statistical Monitoring of Distribution-free Data Streams

In industrial applications, the continuously growing development of multi-sensor approaches, together with the trend of creating data-rich environments, are straining the effectiveness of the traditional Statistical Process Control (SPC) tools. Industrial data streams frequently violate the statistical assumptions on which SPC tools are based, presenting non-normal or even mixture distributions, strong autocorrelation and complex noise patterns.To tackle these challenges, novel nonparametric approaches are required. Machine learning techniques are suitable to deal with distributional assumption violations and to cope with complex data patterns. Recent studies showed that those methods can be used in quality control problems by exploiting only in-control data for training (such a learning paradigm is also known as “one-class-classification”).In recent studies, the use of distribution-free multivariate SPC methods was proposed, based on unsupervised statistical learning tools, pointing out the difficulty of defining suitable control regions for non-normal data. In this paper, a Self-Organizing Map (SOM) based monitoring approach is presented. The SOM is an automatic data-analysis method, widely applied in recent works to clustering and data exploration problems. A very interesting feature of this method consists of its capability of providing a computationally efficient way to estimate a data-adaptive control region, even in the presence of high dimensional problems. Nevertheless, very few authors adopted the SOM in an SPC monitoring strategy. The aim of this work is to exploit the SOM network architecture, and proposing a network design approach that suites the SPC needs. A comparison study is presented, in which the process monitoring performances are compared against literature benchmark methods. The comparison framework is based on both simulated data and real data from a roll grinding application.

Some study on statistical process control of complex data

Statistical process control (SPC) has been widely used to monitor various industrial processes by using statistical methods and techniques, to improve and guarantee the quality of production. SPC to monitor and control the quality of such data-rich processes remains in many challenging problems. In this dissertation, we aim to address the problems with the nature mentioned above through taking advantage of modern resources. We focus on the following topics: profile monitoring and diagnosis, control charts under drift shift, multivariate SPC, and multistage process monitoring and diagnosis. We introduce and develop some new methodologies, with the help of statistical computation, to tackle these important but quite challenging problems.

Statistical Performance of a Control Chart for Individual Observations Monitoring the Ratio of Two Normal Variables

Statistical Process Control monitoring of the ratio Z of two normal variables X and Y has received too little attention in quality control literature. Several applications dealing with monitoring the ratio Z can be found in the industrial sector, when quality control of products consisting of several raw materials calls for monitoring their proportions (ratios) within a product. Tables about the statistical performance of these charts are still not available. This paper investigates the statistical performance of a Phase II Shewhart control chart monitoring the ratio of two normal variables in the case of individual observations. The obtained results show that the performance of the proposed chart is a function of the distribution parameters of the two normal variables. In particular, the Shewhart chart monitoring the ratio Z outperforms the (p = 2) multivariate T2 control chart when a process shift affects the in‐control mean of X or, alternatively, of Y and the correlation among X and Y is high and when the in‐control means of X and Y shift contemporarily to opposite directions. The sensitivity of the proposed chart to a shift of the in‐control dispersion has been investigated, too. We also show that the standardization of the two variables before computing their ratio is not a good practice due to a significant loss in the chart's statistical performance. An illustrative example from the food industry details the implementation of the ratio control chart. Copyright © 2013 John Wiley & Sons, Ltd.

Modeling and Monitoring Ecological Systems—A Statistical Process Control Approach

Statistical process control monitoring of nonlinear relationships (profiles) has been the subject of much research recently. While attention is primarily given to the statistical aspects of the monitoring techniques, little effort has been devoted to developing a general modeling approach that would introduce ‘uniformity of practice’ in modeling nonlinear profiles (analogously with the three‐sigma limits of Shewhart control charts). In this article, we use response modeling methodology (RMM) to demonstrate implementation of this approach to statistical process control monitoring of ecological relationships. Using 10 ecological models that have appeared in the literature, it is first shown that RMM models can replace (approximate) current ecological models with negligible loss in accuracy. Computer simulation is then used to demonstrate that estimated RMM models and estimated data generating ecological models achieve goodness‐of‐fit that is practically indistinguishable from one another. A regression‐adjusted control scheme, based on control charts for the predicted median and for residuals variation, is developed and demonstrated for three types of ‘out of control’ scenarios. Copyright © 2013 John Wiley & Sons, Ltd.

Using statistical process control (SPC) charts for monitoring of surgical performance in vascular surgery: A case study and comparison of two monitoring methods

Background: the technique of prospective monitoring of surgical performance has replaced the traditional audit models in different clinical settings. Risk-adjusted cumulative sum (CUSUM)-type charts and variable life-adjusted display (VLAD) charts are of special interest for quality improvement Method: some 25129 patients on the national vascular database who underwent abdominal aortic aneurysm repair were analysed. A riskadjusted CUSUM chart, a risk-adjusted sequential probability ratio test (SPRT) chart and a VLAD chart with prediction limits chart were used to detect excess deaths. Results: control charts from two centres are shown in order to illustrate the main features of SPC monitoring systems. A risk-adjusted CUSUM model is shown and is comparedwith non-risk adjusted CUSUM and VLAD techniques. Selecting the control limit based on the simulation results of average run length using the method of fractional polynomials to produce a closed-form relationship between the average run length, control limit, and acceptable rate of failure are also described. Conclusion: risk-adjusted CUSUM technique are shown to be reliable, accurate and intuitive technique that can reliably detect outliers in major vascular surgery.

SU-E-T-53: Statistical Process Control Methodologies for Predictive Maintenance of Linear Accelerator Beam Quality

Purpose: This study prospectively applies statistical process control (SPC) methods as a predictive maintenance tool in linear acceleratorphoton beam quality. Methods: Steering coil currents (SCC) are sampled and stored daily during morning warm‐up. The transverse and radial ‐ positioning and angle SCC for photon beams were evaluated using average and range (Xbar‐R) process control charts (PCC). The weekly average and range values (subgroup n=5) for each SCC was used to develop the PCC. Control limits were calculated using the first sixteen subgroups. Run charts of the daily SCC values were maintained and updated weekly. PCC high alarm action limit was set at six standard deviations. Six subgroups in a row all increasing or decreasing were a low alarm indicator. A sustained high alarm of 3 subgroups in conjunction with a low alarm was used as our action threshold (i.e. independent verification of beam flatness and symmetry constancy). Results: Data collection commenced September 2010, following beam steering adjustments during annual calibration. Only alarms received following establishment of limits (week sixteen) were considered valid indicators for deviation or an uncontrolled process. A high alarm was first detected on Jan 25 (15 MV — transverse position). Simulated intervention was triggered by 6 MV — radial angle SCC on February 18th. Beam scans taken and compared to those from the annual calibration indicated a change in symmetry in the transverse plane (0.6% ‐ 6 MV and 1.0% ‐ 15 MV) while the flatness remained effectively unchanged (<0.5%). There were no changes noted in the radial plane for either energy. Conclusions: SPC techniques are able to effectively detect variations in beam steering currents. SPC monitoring of beam steering has the capability to ensure AAPM TG‐142 constancy guidelines of +/− 1% are maintained. Further investigation is required to develop consistent intervention guidelines.

Integrated APC-controlled SPC monitoring chart for quality improvement

There are two widely used process control techniques for the reduction of process output variability. The first technique is automatic process control (APC) that adjusts the process using information about its current level or deviation from a desired target. The APC actions for process adjustments are achieved by the minimum mean square estimate (MMSE) controller or proportional, integral and derivative (PID) controller which minimize the output deviations from the quality target. The MMSE controller is optimal in terms of minimizing mean squared residual errors when the model and its parameters are exactly known. Whereas the PID controller is very efficient and also robust against non-stationarity due to the fact that it can continuously adjust the process whenever the data is auto-correlated. The second technique is statistical process control (SPC) which utilizes control charts. The goal of SPC for improving quality is to monitor and detect process variability, so that the special causes of the process shifting are investigated. While SPC has been successfully used in industry for identifying and eliminating the assignable cause of variations, APC techniques are widely employed in the continuous process industry to reduce common cause variations. For an improved performance of the process for the industry practitioner, both the monitoring and the adjustments of process are needed to receive the full benefit of each approach. Recently, integration of APC and SPC successfully resulted in the reduction of process output variability and improved process efficiency. In this paper, we integrate SPC and APC for various types of industries including liquefied natural gas (LNG) processes. By applying both the statistical process control and the advanced process control to a process we can dramatically improve the quality of process output. Both statistical process control and automatic process control techniques have been widely applied in industry to detect causes of variability by monitoring the key variables in the process. We investigate both techniques, their integration and methods for shift detection in the process for the monitoring of a process.

Maîtrise statistique des processus appliquée aux contrôles avant traitement par dosimétrie portale en radiothérapie conformationnelle avec modulation d’intensité

Purpose The first purpose of this study was to illustrate the contribution of statistical process control for a better security in intensity modulated radiotherapy (IMRT) treatments. This improvement is possible by controlling the dose delivery process, characterized by pretreatment quality control results. So, it is necessary to put under control portal dosimetry measurements (currently, the ionisation chamber measurements were already monitored by statistical process control thanks to statistical process control tools). The second objective was to state whether it is possible to substitute ionisation chamber with portal dosimetry in order to optimize time devoted to pretreatment quality control. Patients and methods At Alexis-Vautrin center, pretreatment quality controls in IMRT for prostate and head and neck treatments were performed for each beam of each patient. These controls were made with an ionisation chamber, which is the reference detector for the absolute dose measurement, and with portal dosimetry for the verification of dose distribution. Statistical process control is a statistical analysis method, coming from industry, used to control and improve the studied process quality. It uses graphic tools as control maps to follow-up process, warning the operator in case of failure, and quantitative tools to evaluate the process toward its ability to respect guidelines: this is the capability study. The study was performed on 450 head and neck beams and on 100 prostate beams. Results Control charts, showing drifts, both slow and weak, and also both strong and fast, of mean and standard deviation have been established and have shown special cause introduced (manual shift of the leaf gap of the multileaf collimator). Correlation between dose measured at one point, given with the EPID and the ionisation chamber has been evaluated at more than 97% and disagreement cases between the two measurements were identified. Conclusion The study allowed to demonstrate the feasibility to reduce the time devoted to pretreatment controls, by substituting the ionisation chamber's measurements with those performed with EPID, and also that a statistical process control monitoring of data brought security guarantee.

An SPC monitoring system for cycle-based waveform signals using haar transform

Due to the rapid development of computer and sensing technology, many measurements of process variables are readily available in manufacturing processes. These measurements carry a large amount of information about process conditions. It is highly desirable to develop a process monitoring and diagnosis methodology that can utilize this information. In this paper, a statistical process control monitoring system is developed for a class of commonly available process measurements-cycle-based waveform signals. This system integrates the statistical process control technology and the Haar wavelet transform. With it, one can not only detect a process change, but also identify the location and estimate the magnitude of the process mean shift within the signal. A case study involving a stamping process demonstrates the effectiveness of the proposed methodology on the monitoring of the profile-type data. Note to Practitioners-Cycle-based signal refers to an analog or digital signal that is obtained through automatic sensing during each operation cycle of a manufacturing process. The cycle-based signal is very common in various manufacturing processes (e.g., forming force in stamping processes, the holding force, and the current signals in spot welding processes, the insertion force in the engine assembly process). In general, cycle-based signals contain rich process information. In this paper, cycle-based signal monitoring will be accomplished by monitoring the wavelet transformation of the signal, instead of monitoring the raw observations themselves. Further, a decision-making technique is developed using the SPC monitoring system to locate where the mean shift occurred and to estimate magnitudes of mean shifts. Thus, this paper presents a generic framework for the enhanced statistical process control technique of cycle-based signals.

Statistical Process Control Based Supervisory Generalized Predictive Control of Thin Film Deposition Processes

This paper presents a supervisory generalized predictive control (GPC) by combining GPC with statistical process control (SPC) for the control of the thin film deposition process. In the supervised GPC, the deposition process is described as an ARMAX model for each production run and GPC is applied to the in situ thickness-sensing data for thickness control. Supervisory strategies, developed from SPC techniques, are used to monitor process changes and estimate the disturbance magnitudes during production. Based on the SPC monitoring results, different supervisory strategies are used to revise the disturbance models and the control law in the GPC to achieve a satisfactory control performance. A case study is provided to demonstrate the developed methodology.

The Changepoint Model for Statistical Process Control

Statistical process control (SPC) requires statistical methodologies that detect changes in the pattern of data over time. The common methodologies, such as Shewhart, cumulative sum (cusum), and exponentially weighted moving average (EWMA) charting, require the in-control values of the process parameters, but these are rarely known accurately. Using estimated parameters, the run length behavior changes randomly from one realization to another, making it impossible to control the run length behavior of any particular chart. A suitable methodology for detecting and diagnosing step changes based on imperfect process knowledge is the unknown-parameter changepoint formulation. Long recognized as a Phase I analysis tool, we argue that it is also highly effective in allowing the user to progress seamlessly from the start of Phase I data gathering through Phase II SPC monitoring. Despite not requiring specification of the post-change process parameter values, its performance is never far short of that of the optimal cusum chart which requires this knowledge, and it is far superior for shifts away from the cusum shift for which the cusum chart is optimal. As another benefit, while changepoint methods are designed for step changes that persist, they are also competitive with the Shewhart chart, the chart of choice for isolated non-sustained special causes.

Modeling the influence of arsenic autodoping on the sheet resistance of epitaxial silicon films and its application to statistical process control (SPC)

An epitaxial layer sheet resistance monitoring procedure has been developed to overcome the convolution between intentional epilayer doping and arsenic autodoping for multiwafer reactors. The procedure models the epilayer as an intentionally phosphorous-doped region plus an arsenic autodoped region by approximating the epilayer as two resistors in parallel. The resulting sheet resistance SPC monitoring procedure is sensitive to shifts in epilayer carrier concentration as well as arsenic autodoping induced by product lots.

The dynamic T 2 chart for monitoring feedback-controlled processes

As manufacturing quality has become a decisive factor in global market competition, statistical quality techniques such as Statistical Process Control (SPC) are widely used in industry. With advances in information, sensing, and data collection technology, large volumes of data are routinely available in processes employing Automatic Process Control (APC) and Engineering Process Control (EPC). Although there is a growing need for SPC monitoring in these feedback-controlled environments, an effective implementation scheme is still lacking. This research provides a monitoring method, termed the dynamic T1 chart that improves the detection of assignable causes in feedback-controlled processes.

SPC Monitoring of MMSE- and Pi-Controlled Processes

To reduce variation in manufacturing processes, traditional statistical process control (SPC) techniques can be applied to monitor automatic process control (APC) controlled processes for detecting assignable cause process variation. In this paper we compare the monitoring of process output and the monitoring of the control action of Minimum-Mean-Squared-Error- and Proportional-Integral-Controlled processes. We show that the robustness property of the PI controller makes it difficult to detect unanticipated mean shifts when the process output is being monitored. We illustrate how the signal-to-noise ratios developed in Jiang, Tsui, and Woodall (2000) can be used to predict the SPC chart performance and help select the appropriate chart for monitoring.

An economic model for integrated APC and SPC control charts

As suggested by Box and Kramer [1] and others, it is possible to reduce both the special cause and common cause variations by applying Statistical Process Control (SPC) methods to monitor the output of an Automatic Process Control (APC) controlled process. In this paper, we develop an economic model for SPC monitoring of APC controlled processes. We also develop an economic loss-based criterion, the Average Quality Cost (AQC), to evaluate the performance of SPC charting methods. The AQC and the traditional average run length of three common SPC charts are investigated and compared.

Statistical monitoring and diagnosis of automatic controlled processes using dynamic PCA

As manufacturing quality has become a decisive factor in competing in a global market, statistical quality techniques such as statistical process control (SPC) are becoming very popular in industries. With advances in sensing and data capture technology, large volumes of data are being routinely collected in automatic controlled processes. There is a growing need for SPC monitoring and diagnosis in these environments, but an effective implementing scheme is still lacking. This research provides an integrated approach to simultaneously monitor and diagnose an automatic controlled process by using dynamic principal component analysis (DPCA) and minimax distance classifier. Through a step-by-step implementation procedure, the proposed scheme is expected to have an impact on many manufacturing industries with automatic process control (APC) or engineering process control (EPC).

An economic model for integrated APC and SPC control charts

As suggested by Box and Kramer [1] and others, it is possible to reduce both the special cause and common cause variations by applying Statistical Process Control (SPC) methods to monitor the output of an Automatic Process Control (APC) controlled process. In this paper, we develop an economic model for SPC monitoring of APC controlled processes. We also develop an economic loss-based criterion, the Average Quality Cost (AQC), to evaluate the performance of SPC charting methods. The AQC and the traditional average run length of three common SPC charts are investigated and compared.