EWMA Charts for Monitoring the Mean and the Autocovariances of Stationary Gaussian Processes

Abstract

In this article simultaneous individual control charts for the mean and the autocovariances of a stationary process are introduced. All control schemes are EWMA (exponentially weighted moving average) charts. A multivariate quality characteristic is considered. It describes the behavior of the mean and the autocovariances. This quantity is transformed to a one-dimensional variable by using the Mahalanobis distance. The control statistic is obtained by exponentially smoothing these variables. Another control procedure is based on a multivariate EWMA recursion applied directly to our multivariate quality characteristic. After that the resulting statistic is transformed to a univariate random variable. Besides modified control charts we consider residual charts. For the residual charts the same procedure is used but the original observations are replaced by the residuals. In an extensive simulation study all control schemes are compared with each other. The target process is assumed to be an ARMA(1, 1) process.     

An ARL-unbiased thinning-based EWMA chart to monitor counts

Abstract

Shewhart control charts are known to be somewhat insensitive to shifts of small and moderate size. Expectedly, alternative control schemes such as the exponentially weighted moving average (EWMA) charts have been proposed to speed up the detection of such shifts. Unfortunately, applying the ordinary EWMA recursion to count data leads to a control statistic no longer with a fixed discrete range. Therefore, we propose a novel chart which relies on a EWMA control statistic where the usual scalar product is replaced by a thinning operation. Actually, we use the new fractional binomial thinning to avoid the typical over-smoothing ascribable to ceiling, rounding, and flooring operations. The properties of this discrete statistic are similar to the ones of its continuous EWMA counterpart and the run length (RL) performance of the associated chart can be computed exactly using the Markov chain approach for independent and identically distributed (i.i.d.) counts. Moreover, this chart is set in such way that: the average run length (ARL) curve attains a maximum in the in-control situation, i.e., the chart is ARL-unbiased; and the in-control ARL is equal to a pre-specified value. We use the R statistical software to provide compelling illustrations of this unconventional EWMA chart and to compare its RL performance with the ones of a few competing control charts for the mean of i.i.d. Poisson counts.     

Ewma charts for multivariate time series

In this paper a muIt,ivariat.e EWMA chart for time series is introduced. In principle, it is a generalization of the control scheme of Lowry et al. (I992) for multivarite indendent observations.

The autocovariances of the EWMA recursion are derived for stationary multivariate time series. IYsing tllese reslllts a co11t.rol chart hased or1 t11 illt.ivariate EWMA recursion is proposed. For a multivariate autoregressive process of order 1, a sufficient. condition is given such that the in-control average run length (ARL) is invariant, withrespect to the covariance of the White Noise process. This scheme is compared with the MEWMA control chart of Lowry et al. (1992) applied to the residuals.

By an extensive Monte carlo study the ARL of both charts are determined for several multivariate autoregressive processses.     

Statistical Surveillance of the Parameters of a One-Factor Cox–Ingersoll–Ross Model

Abstract

In the paper, the tools of statistical process control, and in particular control charts, are applied to sequentially detect a change in the parameters of the Cox–Ingersoll–Ross term-structure model. Different types of multivariate EWMA control charts are introduced and constructed, taking into account the peculiarities of the Cox– Ingersoll–Ross model. The effectiveness of the control charts is analysed on the basis of extensive Monte Carlo simulations for a parameter constellation obtained from a data set on the term-structure in USA. In addition, the paper includes a practical example of a detection of a change in an initially estimated Cox–Ingersoll–Ross model.     

Counting by Weighing: An Alternative Sampling Scheme

Abstract

In the last decades, various methods are applied for evaluating different performance measures of change-point detection schemes. In only some cases—recent examples are Chandrasekaran et al. (Chandrasekaran, S.; English, J.R.; Disney, R.L. Modeling and analysis of EWMA control schemes with variance-adjusted control limits. IIE Transactions 1995, 277, 282–290) and Steiner (Steiner, S.H. EWMA control charts with time-varying control limits and fast initial response. Journal of Quality Technology 1999, 31 (1), 75–86)—EWMA schemes with varying control limits are considered. However, EWMA charts with just these limits are sometimes more appropriate than those with fixed limits. Here, a computational approach is presented which allows to compute the usual performance measures with high precision. The main idea is connected to earlier results of Madsen and Conn (Madsen, R.W.; Conn, P.S. Ergodic behavior for nonnegative kernels. Ann. Probab. 1973, 1, 995–1013), Woodall (Woodall, W.H. The distribution of the run length of one-sided CUSUM procedures for continuous random variables. Technometrics 1983, 25, 295–301), and Waldmann (Waldmann, K.-H. Bounds for the distribution of the run length of geometric moving average charts. J. R. Stat. Soc., Ser. C, Appl. Stat. 1986a, 35, 151–158). Additionally, quantities as the steady-state ARL and the steady-state distribution of the chart statistic can be computed very precisely.     

The Generalized Synthetic Chart

Abstract

The Generalized Synthetic chart is presented and mathematical expressions for its average run length and variance of the run length are developed. The methodology is applied to the EWMA and CUSUM charts and near-optimization procedures are discussed. The synthetic EWMA and CUSUM charts are compared with their standard counterparts, the original synthetic chart, and the Shewhart chart. Significant improvements in detecting power are reported.     

Evaluating properties of variable sampling interval control charts

Standard fixed sampling interval (FSI) control charts take samples from a process at fixed length sampling intervals for purposes of detecting changes in the peocess that may affect the quality of the output. Variable sampling interval (VSI) control charts vary the sampling interval as a function of what is observed from the process and can detect process changes faster than FSI control charts. Evaluation of properties of VSI control charts requires extensions of methods that have been developed for FSI control Control charts. A unified treatment of two widely used methods, the Markov chain method and the integral equation method. is given for VSI control charts.This unified treatment includes some results which are new in the FSI case. The new methods are used for the numerical evaluation of propertics of exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts.Some general optimality results for the choice fo the sampling intervals are also given.     

A Note on the Aging Properties of the Run Length of Markov-Type Control Charts

Abstract

A change in a production process must be detected quickly so that a corrective action can be taken. Thus, it comes as no surprise that the run length (RL) is usually used to describe the performance of a quality control chart.

This popular performance measure has a phase-type distribution when dealing with Markov-type charts, namely, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts, as opposed to a geometric distribution, when standard Shewhart charts are in use.

In this article, we briefly discuss sufficient conditions on the associated probability transition matrix to deal with run lengths with aging properties such as new better than used in expectation, new better than used, and increasing hazard rate.

We also explore the implications of these aging properties of the run lengths, namely when we decide to confront the in control and out-of-control variances of the run lengths of matched in control Shewhart and Markov-type control charts.     

Improved process monitoring using the CUSUM and EWMA-based multiscale PCA fault detection framework

Process monitoring techniques are of paramount importance in the chemical industry to improve both the product quality and plant safety. Small or incipient irregularities may lead to severe degradation in complex chemical processes, and the conventional process monitoring techniques cannot detect these irregularities. In this study to improve the performance of monitoring, an online multiscale fault detection approach is proposed by integrating multiscale principal component analysis (MSPCA) with cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts. The new Hotelling's T² and square prediction error (SPE) based fault detection indices are proposed to detect the incipient irregularities in the process data. The performance of the proposed fault detection methods was tested for simulated data obtained from the CSTR system and compared to that of conventional PCA and MSPCA based methods. The results demonstrate that the proposed EWMA based MSPCA fault detection method was successful in detecting the faults. Moreover, a comparative study shows that the SPE-EWMA monitoring index exhibits a better performance with lower values of missed detections ranging from 0% to 0.80% and false alarms ranging from 0% to 21.20%.     

Rigorous design of multipass exchangers when overall heat transfer coefficient is a parabolic function of temperature

The “thermal effectiveness-transfer unit” charts developed by the authors, for multipass exchangers, assume that the overall heat transfer coefficient varies as a parabolic function of temperature; their use can lead to greater accuracy in calculating heat transfer areas.     

An exact method for determining the surface of a countercurrent heat exchanger when the tube side coefficient governs and is a parabolic function of temperature

The “Thermal effectiveness-Transfer unit” charts developed by the authors, for the countercurrent heat exchanger, assume that the overall heat transfer coefficient varies as a parabolic function of temperature; their use can lead to greater accuracy in calculating heat transfer areas.     

Erfassung,Beschaffung und Montage von Rohrleitungsteilen

Assessment, acquisition, and assembly of pipe components . Pipe technology accounts for ca. 30 to 35% of the planning of chemical plant and refineries. The reason for this high proportion lies in the numerous possibilities of variation. Each part must be defined, assessed and executed. The programme system developed consists of an assembly of several individual programmes which utilize available data. The overall procedure, from specification to assembly, is performed or supported by this programme system. The “general text system” (ATS) stores all pipe texts and pipe classes in several languages. With the aid of the “Lurgi piping macro-system” (LUROMAK ) the piping components are processed on the basis of flow charts, assembly plans and isometric drawings. The materials determined are transformed into buying information by the “execution system” (DISPO ). Registration of material entering and leaving stores in the “assembly organization system” (MOS) permits work preparation for assembly on the basis of the resulting stocks. It is also possible to assess the progress of assembly and to prepare costing information. The continuous processing of piping is permitted by a systematic standardization and classification, accomplished in particular by uniform definition of piping components in the ATS programme system.     

Enhancing Controller Performance via Dynamic Data Reconciliation

Measured values of process variables are subject to measurement noise. The presence of measurement noise can result in detuned controllers in order to prevent excessive adjustments of manipulated variables. Digital filters, such as exponentially weighted moving average (EWMA) and moving average (MA) filters, are commonly used to attenuate measurement noise before controllers. In this article, we present another approach, a dynamic data reconciliation (DDR) filter. This filter employs discrete dynamic models that can be phenomenological or empirical, as constraints in reconciling noisy measurements. Simulation results for a storage tank and a distillation column under PI control demonstrate that the DDR filter can significantly reduce propagation of measurement noise inside control loops. It has better performance than the EWMA and MA filters, so that the overall performance of the control system is enhanced.     

A GRAPHICAL DESIGN METHOD FOR A PARTIAL SOLAR DRYER FOR CORN

ABSTRACT

This paper presents the application of a design method for a partial solar heating system of polyvalent modular dryers called “GJ-ABAQUE” to the drying of thick layers of grains.

This method is based on the use of charts or polynomial correlations. In the actual case where the drying air is not recycled, we only need one chart which allows one to determine the fraction of the monthly heating load supply by solar energy as a function of two dimensionless parameters. The latter implies the use of monthly average radiation data, the collector surface and estimates of drying loads.

The “GJ-ABAQUE” method was applied for drying 777 kg of corn, corresponding to 1 m³ of fresh product, in a thick layer in each modular dryer.     

REFINED METHOD OF CONTROL OF CORDINESS AND WORKABILITY OF GLASS DURING PRODUCTION*

Many glass plants obtain daily measurements of the density or specific gravity of the glass in each furnace. Small daily fluctuations of about ±0.0010 density unit are usually taken for granted, while pronounced changes within a two- or three-day period are a matter of concern; but heretofore neither criteria of permissible variability nor rules for interpretation of the data have been in general use. In the present work, the control-chart method of statistical analysis of past data has been applied to data from ten glass furnaces. Small daily fluctuations of density are found to be statistical in character, and the predominant cause of large variations is found to be in the batch house. The rational subgroup sample to be used in analyzing such variations and in operating a control chart is found to be a subgroup of three consecutive daily density values obtained from a particular furnace. Using this subgroup, the average 3-day range of density for the ten furnaces varied from 0.0006 to 0.0023, and the corresponding 3-sigma limits for daily variation from the central line density were ±0.0011 to ±0.0040. A typical value for the average 3-day range of density is 0.0012 and a value no larger than this is a reasonable goal for a glass container plant. The use of control charts for maintaining a state of statistical control of density during production is illustrated for four furnaces over a 2- to 6-month period. Many assignable causes of variation were found in the batch house, usually in the scales; other assignable causes were changes in cullet and in raw materials, changes in firing of the furnace, and laboratory errors in measurement of the density. Present experience indicates that it is difficult to maintain a state of statistical control with the types of batch-weighing equipment in use in some plants. The importance of control, however, was demonstrated for two furnaces in two different plants by the fact that cordiness increased with increasing 3-day range of density. When the density was not maintained under statistical control in one plant, trouble was experienced with checks in the ware. The use of control charts for keeping lack of control within tolerable limits is discussed for one furnace where the variations were small and the control limits narrow. The range was held under control, but the density showed “trends” and went out of control. In this instance, the 3-sigma control limits for variation of daily values from the central line density were ±0.0011, corresponding to ±0.09% replacement of lime by silica. Inasmuch as composition changes in excess of ±0.09% are tolerable in the present state of the art, a modified control limit corresponding to a composition change of approximately ±0.25% is suggested, the corresponding density limits being ±0.0030. When the 3-sigma limits for density are less than, this value, modified limits may be used, although the 3-sigma limits for range are retained. When the 3-sigma limits are greater than ±0.0030, it is most desirable to maintain strict statistical control, and efforts should be made to reduce the variability; otherwise there may be excessive cordiness and other difficulties in fabrication of the ware. In some instances, a reduction in variability will require major repair of batch handling and weighing equipment or a new batch-house weighing installation. Other subgroup methods and other sources of variability are also discussed. Control charts on density are of practical utility to plants. “Assignable-cause” variations are easily distinguished from unimportant, normal variations. The use of 3-sigma action limits keeps investigation of fluctuations to a minimum, and sets troubleshooting, when it is necessary, on the right track. The charts, furthermore, are a useful guide toward a permanent reduction of the variability. They should be helpful to management in striking an economic balance among tonnage pulled, glass quality, and capital expenditures for improvement of batch mixing and handling and other changes. The time required to maintain a chart for one furnace is about one day for past-data analysis, one minute each day for plotting, and not more than one day per month for current analysis, review, and adjustment.     

Oxidant control and air-oxy switching concepts for CFB furnace operation

Oxy combustion in circulating fluidized bed (CFB) boilers was investigated in this paper. Oxy combustion is a carbon capture and storage technology, which uses oxygen and recirculated flue gas (RFG) instead of air as an oxidant. Air and oxy combustion were compared through physical considerations and simulations, focusing on process dynamics, transients and control. The oxidant specific heat capacity and density are elevated in oxy combustion, which leads to slower temperature dynamics. Flue gas recirculation introduces internal feedback dynamics to the process. The possibility to adjust the RFG and oxygen flows separately gives an additional degree of freedom for control. In the simulations, “direct” and “sequenced” switches between air- and oxy-firing were compared. Fast “direct” switches with simultaneous ramping of all inputs should be preferred due to the resulting smooth temperature responses. If these process input changes are unfeasible, the fuel should be altered after the gaseous flows (“sequenced” method).     

POROSITY: V. RECOMMENDED PROCEDURES FOR DETERMINING POROSITY BY METHODS OF ABSORPTION

Detailed Procedure. —For shaped test pieces details of the procedure are given under the headings. “Preparation of Test Piece.”“Determination of Dry Weight,”“The Absorption Apparatus,”“Preparation of Standard Vaseline,”“Saturation Procedure,”“Calculation,” and “True Density.” A Pycnometer Method. —A new and accurate method, which is applicable equally to shaped test pieces or to granular material, is described. Among other advantages it gives the operator control over the max. size opening which he desires to class as part of the pore space. It also can be made to indicate directly the necessary soaking period.     

Shape memory gels made by the modulated gel technology

Shape memory gels based on interpenetrating only part of one gel network with another gel network have been synthesized. These gels consist of two parts: a control element, which is responsive to a designated environmental stimulus, and a nonresponsive substrate element. By designing the pattern in the gelation process, a variety of shapes are obtained including “spiral,” “square,” “fish,” “numbers,” “alphabets,” and “tube.” The change between two different shapes can be controlled by external stimuli such as temperature and is reversible. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 63: 1173–1178, 1997     

Optimal Surveillance Based on Exponentially Weighted Moving Averages

Abstract

Statistical surveillance is used to detect an important change in a process as soon as possible after it has occurred. The exponentially weighted moving averages (EWMA) method is used in industry, economics, and medicine. Three optimality criteria of surveillance are studied. The average run length (ARL) criterion violates commonly accepted inference principles, and the drawbacks are demonstrated. The expected delay criterion is based on the minimal expected delay from change to detection. The full likelihood ratio method is optimal according to this criterion. Approximations of this method turn out to be modifications of the EWMA method. The approximations lead to a formula for the optimal value of the smoothing parameter of the EWMA statistic. The usefulness of this formula is shown. It is demonstrated that, for EWMA, the minimax criterion agrees well with that of the ED criterion but not with that of the ARL criterion.