Residual Control Charts Research Articles

Principal component analysis for the early detection of mastitis and lameness in dairy cows

This investigation analysed the applicability of principal component analysis (PCA), a latent variable method, for the early detection of mastitis and lameness. Data used were recorded on the Karkendamm dairy research farm between August 2008 and December 2010. For mastitis and lameness detection, data of 338 and 315 cows in their first 200d in milk were analysed, respectively. Mastitis as well as lameness were specified according to veterinary treatments. Diseases were defined as disease blocks. The different definitions used (two for mastitis, three for lameness) varied solely in the sequence length of the blocks. Only the days before the treatment were included in the blocks. Milk electrical conductivity, milk yield and feeding patterns (feed intake, number of feeding visits and time at the trough) were used for recognition of mastitis. Pedometer activity and feeding patterns were utilised for lameness detection. To develop and verify the PCA model, the mastitis and the lameness datasets were divided into training and test datasets. PCA extracted uncorrelated principle components (PC) by linear transformations of the raw data so that the first few PCs captured most of the variations in the original dataset. For process monitoring and disease detection, these resulting PCs were applied to the Hotelling's T 2 chart and to the residual control chart. The results show that block sensitivity of mastitis detection ranged from 77·4 to 83·3%, whilst specificity was around 76·7%. The error rates were around 98·9%. For lameness detection, the block sensitivity ranged from 73·8 to 87·8% while the obtained specificities were between 54·8 and 61·9%. The error rates varied from 87·8 to 89·2%. In conclusion, PCA seems to be not yet transferable into practical usage. Results could probably be improved if different traits and more informative sensor data are included in the analysis.

Process Monitoring and Adjustment Based on Optimal RBF Network

Modern complex manufacturing process output data showed high autocorrelation, resulting in the output of the process to deviate from the design target , or that false alarms increasd in traditional control chart in monitoring process. Statistical Process Control (SPC) and Automatic process control (APC) are main methods of industrial processes. Study based on the optimization of radial basis (Radial Basis Funtion RBF) neural network integrated SPC/APC quality control model, the forecast MMSE controller based on optimal radial basis function networks were utilized to adjut process of productive process output, and residual control charts were utilized to monitor process output after adjustment. Results show that optimal RBF network can improve forecast accuracy and adjustment effect, eliminate effectively process output autocorrelation. The residual control chart will in steady state and with small fluctuation. Intergrated SPC/APC quality control model based on optimal radial basis function can eliminate process fluctuation effectively and guaranteeproduct stable quality in process quality control.

Applying Residual Control Charts to Identify the False Alarms in a TFT-LCD Manufacturing Process

Statistical Process Control (SPC) is widely applied to monitor and improve highly integrated and automated manufacturing processes. Adopting proper SPC charts and corresponding detection mechanisms is crucial for a TFT-LCD manufacturing process. This study conducts an empirical study of highly complex TFT-LCD manufacturing processes to identify the most suitable SPC method. The TFT-LCD manufacturing process is generally divided into three main procedures, namely Array Engineering to create the TFT array, Cell Engineering to join the TFT array, liquid crystal and color filter together, and Module Engineering to integrate PCB and semiconductor chips into final products. The crucial step in Cell Enginee ring is injecting the liquid crystal into the layer between the TFT array and color filter substrates and the thickness of the layer is the ma in control target. Applying traditional Shewhart and EWMA control charts to real TFT-LCD manufacturing data reveals a significan t false alarm rate, and these false alarms can adversely impact manufacturing efficiency. Based on time series analysis, this study prop oses a residual control chart using an AR(1) model to avoid false alarms that could obstruct TFT-LCD manufacturing flow. The res ults of the proposed approach provide a useful guideline for improving the TFT-LCD manufacturing.

A COMPARISON OF PERFORMANCE OF RESIDUAL CONTROL CHARTS FOR TREND STATIONARY AR(p) PROCESSES

The main goal of this paper is to implement Statistical Process Control (SPC) with Residual Control Charts. In real life applications, such as in industries or manufacturing, many processes are described by autocorrelated observations. In addition to autocorrelation, some types of industrial processes also exhibit a particular kind of trend behavior. A typical example of process with autocorrelations arises in chemical processes. One of the main characteristics of a control chart are the Average Run Length (ARL0) (mean of false alarm times) and the Average Delay time (ARL1) (mean delay of true alarm times). The main parameter observed for a given process is the mean shift. If a process has no mean shift, then the ARL0 should be sufficiently large. On the opposite side, when a mean shift occurs the ARL1 should be small in order to indicate the mean shift quickly. We compared the performance of the Shewhart x, EWMA, and GMA residual control charts for autocorrelation observations with upward/downward linear trend. These comparisons are made for different magnitudes of the mean shift and various levels of autocorrelation. AMS Subject Classification: 60A05

Statistical process control of mortality series in the Australian and New Zealand Intensive Care Society (ANZICS) adult patient database: implications of the data generating process

BackgroundStatistical process control (SPC), an industrial sphere initiative, has recently been applied in health care and public health surveillance. SPC methods assume independent observations and process autocorrelation has been associated with increase in false alarm frequency.MethodsMonthly mean raw mortality (at hospital discharge) time series, 1995–2009, at the individual Intensive Care unit (ICU) level, were generated from the Australia and New Zealand Intensive Care Society adult patient database. Evidence for series (i) autocorrelation and seasonality was demonstrated using (partial)-autocorrelation ((P)ACF) function displays and classical series decomposition and (ii) “in-control” status was sought using risk-adjusted (RA) exponentially weighted moving average (EWMA) control limits (3 sigma). Risk adjustment was achieved using a random coefficient (intercept as ICU site and slope as APACHE III score) logistic regression model, generating an expected mortality series. Application of time-series to an exemplar complete ICU series (1995-(end)2009) was via Box-Jenkins methodology: autoregressive moving average (ARMA) and (G)ARCH ((Generalised) Autoregressive Conditional Heteroscedasticity) models, the latter addressing volatility of the series variance.ResultsThe overall data set, 1995-2009, consisted of 491324 records from 137 ICU sites; average raw mortality was 14.07%; average(SD) raw and expected mortalities ranged from 0.012(0.113) and 0.013(0.045) to 0.296(0.457) and 0.278(0.247) respectively. For the raw mortality series: 71 sites had continuous data for assessment up to or beyond lag40 and 35% had autocorrelation through to lag40; and of 36 sites with continuous data for ≥ 72 months, all demonstrated marked seasonality. Similar numbers and percentages were seen with the expected series. Out-of-control signalling was evident for the raw mortality series with respect to RA-EWMA control limits; a seasonal ARMA model, with GARCH effects, displayed white-noise residuals which were in-control with respect to EWMA control limits and one-step prediction error limits (3SE). The expected series was modelled with a multiplicative seasonal autoregressive model.ConclusionsThe data generating process of monthly raw mortality series at the ICU level displayed autocorrelation, seasonality and volatility. False-positive signalling of the raw mortality series was evident with respect to RA-EWMA control limits. A time series approach using residual control charts resolved these issues.

ARL performance of residual control charts for trend AR(1) process: A case study on peroxide values of stored vegetable oil

For the purpose of process control, quality assurance engineers in a vegetable oil factory wonder the performance of the Shewhart, CUSUM, and EWMA residual control charts for peroxide values that show both serial autocorrelation between adjacent observations (autocorrelation) and upward linear trend. To deal with autocorrelated process data, a primary method is to apply these charts to the uncorrelated residuals of an appropriate time series model fitted to the data. In the relevant literature, although performances of the residual charts have been widely studied for autocorrelated processes, there exists no study that shows how these charts’ performances change by the addition of a particular type of trend in the autocorrelated data. In the present paper, average run length performances of these charts are computed for peroxide data from two batches, for which trend stationary first order autoregressive (trend AR(1) for short) model is a representative model. Key words: Statistical process control, autocorrelation, peroxide value, vegetable oil, trend AR(1) model.

Average Run Lengths in Shewhart Type Charts for 2-Order Autoregressive Process

In this paper the average run length is adopted as the tool to describe the performance of control charts. The respective methods for calculating the average run length of the modified Shewhart control chart and the Shewhart residual control chart for 2-order autoregressive process are derived and shown in detail. By the proposed approach some numerical results of average run lengths of both Shewhart type charts are formulated and discussed. We analyze and compare that the influence of the correlation coefficients of the 2-order autoregressive process on the performance of both charts based on the estimated data. Several clear and main points of the issue are summed up. Lastly, we give some recommendations for the choice of both Shewhart type control schemes.

Monitoring heterogeneous serially correlated usage behavior in subscription-based services

Effective monitoring of usage behavior necessitates applying accurate stochastic models to represent customer heterogeneous time-dependent behavior. In this research, it is assumed that the sequence of customer visits over a subscription period occurs based on the Poisson process, while usage at each purchase occasion follows an autoregressive Bernoulli model of first order. The autocorrelated observations are derived from a two-state Markov chain model. Generalized linear models are employed to describe heterogeneous behavior across customers. In order to monitor the number of visits as well as the fraction of visits eventuated in a purchase, control statistics are defined on the basis of generalized likelihood ratio (GLR) test. Furthermore, in the case of the marginal logistic model for dependent observations, a chi-square test statistic based on the asymptotic multivariate normal distribution of quasi-likelihood estimates is employed. Performances of the monitoring schemes are compared with an illustrative case provided by simulation. Results indicate that the adjusted Shewhart c chart resembles the deviance residual control chart for monitoring the frequency of customer visit. On the other hand, the GLR statistic based on the conditional logistic regression is more powerful in detecting unnatural usage behavior when compared with the chi-square control statistic based on the marginal logistic model.

Support vector regression based residual control charts

Control charts for residuals, based on the regression model, require a robust fitting technique for minimizing the error resulting from the fitted model. However, in the multivariate case, when the number of variables is high and data become complex, traditional fitting techniques, such as ordinary least squares (OLS), lose efficiency. In this paper, support vector regression (SVR) is used to construct robust control charts for residuals, called SVR-chart. This choice is based on the fact that the SVR is designed to minimize the structural error whereas other techniques minimize the empirical error. An application shows that SVR methods gives competitive results in comparison with the OLS and the partial least squares method, in terms of standard deviation of the error prediction and the standard error of performance. A sensitivity study is conducted to evaluate the SVR-chart performance based on the average run length (ARL) and showed that the SVR-chart has the best ARL behaviour in comparison with the other residuals control charts.

Bootstrap-based design of residual control charts

One approach to monitoring autocorrelated data consists in applying a control chart to the residuals of a time series model estimated from process observations. Recent research shows that the impact of estimation error on the run length properties of the resulting charts is not negligible. In this paper a general strategy for implementing residual-based control schemes is investigated. The designing procedure uses the AR-sieve approximation assuming that the process allows an autoregressive representation of order infinity. The run length distribution is estimated using bootstrap resampling in order to account for uncertainty in the estimated parameters. Control limits that satisfy a given constraint on the false alarm rate are computed via stochastic approximation. The proposed procedure is investigated for three residual-based control charts: generalized likelihood ratio, cumulative sum and exponentially weighted moving average. Results show that the bootstrap approach safeguards against an undesirably high rate of false alarms. In addition, the out-of-control bootstrap chart sensitivity seems to be comparable to that of charts designed under the assumption that the estimated model is equal to the true generating process. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resource: Appendix]

Models for monitoring wind farm power

Different models for monitoring wind farm power output are considered. Data mining and evolutionary computation are integrated for building the models for prediction and monitoring. Different models using wind speed as input to predict the total power output of a wind farm are compared and analyzed. The k-nearest neighbor model, combined with the principal component analysis approach, outperforms other models studied in this research. However, this model performs poorly when the conditions of the wind farm are abnormal. The latter implies that the original data contains many noisy points that need to be filtered. An evolutionary computation algorithm is used to build a nonlinear parametric model to monitor the wind farm performance. This model filters the outliers according to the residual approach and control charts. The k-nearest neighbor model produces good performance for the wind farm operating in normal conditions.

Support vector regression based residual MCUSUM control chart for autocorrelated process

Traditional control charts assume that processes are serially independent, and autocorrelation among variables makes them unreliable. To handle this problem alternative charts estimate the time series structure of the process and use residuals for control. While in previous studies, estimation is performed using classical statistical methods or artificial neural networks, this study proposes to apply support vector regression (SVR) method for construction of a residuals Multivariate Cumulative Sum (MCUSUM) control chart, for monitoring changes in the process mean vector. Using simulated data, analysis and comparison of the proposed control chart with other charts show that SVR-based control chart is more effective in detecting small shifts in the mean vector. This fact makes the proposed chart a very promising method since the MCUSUM chart is, in practice, designed to detect small shifts in the process parameters.

Monitoring long‐memory air quality data using ARFIMA model

AbstractStatistical control chart is commonly used in the industry to help ensure stability of manufacturing process and it can also be used to monitor the environmental data, such as industrial waste or effluent of manufacturing process. However, control chart needs to be modified if the set of environmental data exhibits the property of long memory. In this paper, a control chart for autocorrelated data using autoregressive fractionally integrated moving‐average (ARFIMA) model is proposed to monitor the long‐memory air quality data. Finally, we use the air quality data of Taiwan as examples to compare the difference between ARFIMA and autoregressive integrated moving‐average (ARIMA) models. The results show that residual control charts using ARFIMA models are more appropriate than those using ARIMA models. Copyright © 2007 John Wiley & Sons, Ltd.

On SPC for Short Run Autocorrelated Data

ABSTRACT The existence of a large amount of historical data set and the assumption that process observations are independent and identically distributed are two necessary conditions to effectively and efficiently implement traditional control charts. In many manufacturing environments there is neither enough observations nor the data are i.i.d. In this article we show that the use of Q statistics in conjunction with residuals control charts is an appropriate Statistical Process Control (SPC) tool for short run autocorrelated data. A performance analysis is conducted to compare he proposed method to traditional residuals control charts. Results indicate that residual control charts provide much better shift detection properties than charts based on Q statistics. However, as the under control data set increases, the superiority of residual charts decreases.

Residual Control Charts for Improving Changeover Productivity

Although statistical control charts have been popularly used in monitoring process quality, the concepts of statistical control are essentially suited to the improvement of productivity in virtually any area of business. This article presents a new statistical control chart, the residual control chart, which was employed to improve machine changeover productivity in a textile manufacturing company. To control productivity of various manned operations, the authors identified variation due to the performance of technicians while controlling for the effect of other factors. Instead of making numerous charts for individual categories, the proposed control chart reduces the number of charts, while still blocking out the effect of extraneous factors. The residual chart may be used to help managers balance workloads, plan training programs, and/or assist in conducting performance appraisals.

Shifts recognition in correlated process data using a neural network

Traditional statistical process control (SPC) techniques of control charting are not applicable in many process industries because data from these facilities are autocorrelated. Therefore the reduction in process variability obtained through the use of SPC techniques has not been realized in process industries. Techniques are needed to serve the same functions as SPC control charts, which are to identify shifts in correlated parameters. Neural networks are a potential tool for identifying shifts in correlated process parameters, as data independence is not an assumption of neural network theory. In this research, a back-propagation neural network is utilized to identify shifts in process parameter values from AR (1) time series models with varying values of the autocorrelation coefficient φ. To find the appropriate number of input nodes for use in a neural network model, the all-possible-regression selection procedure is applied. In addition, time series residual control charts are also developed for the data sets for comparison. As the results reveal, networks were successful at separating data that were shifted one, two and three standard deviations from non-shifted data for generated process data. The SPC control charts were not able to identify the same process shifts. In the other words, the neural networks can be used to identify shifts in process parameters. Therefore, it is allowing improved control in manufacturing processes that generate correlated process data.

Shifts recognition in correlated process data using a neural network

Traditional statistical process control (SPC) techniques of control charting are not applicable in many process industries because data from these facilities are autocorrelated. Therefore the reduction in process variability obtained through the use of SPC techniques has not been realized in process industries. Techniques are needed to serve the same functions as SPC control charts, which are to identify shifts in correlated parameters. Neural networks are a potential tool for identifying shifts in correlated process parameters, as data independence is not an assumption of neural network theory. In this research, a back-propagation neural network is utilized to identify shifts in process parameter values from AR (1) time series models with varying values of the autocorrelation coefficient φ. To find the appropriate number of input nodes for use in a neural network model, the all-possible-regression selection procedure is applied. In addition, time series residual control charts are also developed for the data sets for comparison. As the results reveal, networks were successful at separating data that were shifted one, two and three standard deviations from non-shifted data for generated process data. The SPC control charts were not able to identify the same process shifts. In the other words, the neural networks can be used to identify shifts in process parameters. Therefore, it is allowing improved control in manufacturing processes that generate correlated process data.

SHIFTS RECOGNITION IN CORRELATED MANUFACTURING PROCESS PARAMETERS USING NEURAL NETWORK

ABSTRACT Because of the existence of the autocorrelation in the data series, traditional statistical process control (SPC) techniques of control charting are not applicable in many process industries. Therefore how to reduce the process variability obtained through the use of SPC techniques has been discussed for years in process industries. Techniques are needed to serve the same functions as SPC control charts that are to identify shifts, in correlated parameters. Neural networks are a massively parallel system and are a potential tool that can be used to identify shifts in correlated process parameters. In this research, backpropagation neural networks are developed to identify shifts in process parameter values from papermaking and viscosity data set available in literature. For finding the appropriate number of input nodes to use in a neural network model, the all-possible-regression selection procedure is applied. For comparison, the time series residual control charts are also developed for the data sets. As the results reveal, networks were successful at identifying data that were shifted one, one and half, and two standard deviations from non-shifted data for both utilized cases. The SPC control charts were not able to classify the same process shifts. In the other words, the neural networks outperform than the traditional SPC approaches in identifying shifts in process parameters. Therefore, it is allowing improved control in manufacturing processes that generate correlated process data.

Using radial basis function neural networks to recognize shifts in correlated manufacturing process parameters

Traditional statistical process control (SPC) techniues of control charting are not applicable in many process industries because data from these facilities are autocorrelated. Therefore the reduction in process variability obtained through the use of SPC techniques has not been realized in process industries. Techniques are needed to serve the same function as SPC control charts, that is to identify process shifts, in correlated parameters. Radial basis function neural networks were developed to identify shifts in process parameter values from papermaking and viscosity data sets available in the literature. Time series residual control charts were also developed for the data sets. Networks were successful at separating data that were shifted 1.5 and 2 standard deviations from nonshifted data for both the papermaking and viscosity parameter values. The network developed on the basis of the papermaking data set was also able to separate shifts of 1 standard deviation from nonshifted data. The SPC control charts were not able to identify the same process shifts. The radial basis function neural networks can be used to identify shifts in process parameters, thus allowing improved process control in manufacturing processes that generate correlated process data.

Detection capability of residual control chart for stationary process data

Summary In recent years, methods for dealing with autocorrelated data in the statistical process control environment have been proposed. A primary method is based on modeling the process data and applying control charts to the residuals. However, the residual charts do not have the same properties as the traditional charts. In the literature, there has been no systematic study on the detection capability of the residual chart for the stationary processes. The article develops a measure of the detection capability of the residual chart for the general stationary processes. Conditions under which the residual chart reduces or increases the detection capability are given. The relationships between the detection capability and the average run length of the residual chart are also established.