EWMA Charts Research Articles

Explicit Formula of ARL for SMA(Q)L with Exponential White Noise on EWMA Chart

Explicit Formula of ARL for SMA(Q)L with Exponential White Noise on EWMA Chart

Economic and economic-statistical designs of the side sensitive group runs chart

The idea of proposing the economic and economic-statistical designs of the side sensitive group runs (SSGR) chart is presented in this paper. In the economic design, a simplified algorithm is used to search for the optimal design parameters that minimize the expected hourly cost. Nevertheless, this design has a major weakness, where it overlooks the statistical performance of the control chart. Therefore, in order to improve the effectiveness of the control chart in detecting process shifts, the economic-statistical design takes into account the statistical properties while the cost is minimized by placing statistical constraints upon the cost model of the economic design. Besides formulating the economic and economic-statistical designs based on the average run length (ARL), the economic and economic-statistical designs of the SSGR chart are also formulated based on the expected average run length (EARL) since the process shift size is usually unknown in real situations. In this paper, the sensitivity analyses of the optimal cost and the optimal design parameters are implemented for various input parameters. The effects of misspecification of the shift size on the performance of the SSGR chart are also illustrated based on numerical examples for different input parameters. This paper will also look at whether the SSGR chart performs economically better than the Shewhart X‾, synthetic, group runs (GR) and EWMA charts in the economic-statistical design based on the EARL. From the results of comparison, it is shown that the economic performance of the SSGR chart is better than that of the other four control charts in most practical situations.

A New Control Technique with Quality Characteristic Shifting with Time

In this paper, a new quality control technique is discussed, in which the quality characteristic shifts with time. A trends semi-circle control chart is proposed to control this type of processes effectively. An optimization model is suggested to determine the optimal interval of adjustment. We also discuss the average run length of the proposed control chart and the extension to the EWMA chart. An example is used to illustrate its application in a production process. Copyright © 2015 John Wiley & Sons, Ltd.

Identifying the time of a step change in AR(1) auto-correlated simple linear profiles

Assuming a first-order auto-regressive model for the auto-correlation structure between observations, in this paper, a transformation method is first employed to eliminate the effect of auto-correlation. Then, a maximum likelihood estimator (MLE) of a step change in the parameters of the transformed model is derived and three separate EWMA control charts are used to monitor the parameters of the profile. The performance of the proposed change-point estimator is next compared to the one of the built-in change-point estimator of EWMA control chart through some simulation experiments. The results show that the proposed MLE of the change point accurately estimates the true change point and outperforms the built-in estimator of EWMA chart for almost all shift values and auto-correlation coefficients, while the built-in estimator of EWMA chart, in general, underestimates the true change point.

Behavior of EWMA type control charts for small smoothing parameters

A general family of EWMA charts is considered for monitoring an arbitrary parameter of the target process. The distribution of the run length is analysed for the case when the smoothing parameter tends to zero. The key impact on the results from the use of the exact variance of the control statistics vs. the asymptotic one and the presence of a head start. For fixed head start, the run lengths for both the exact and asymptotic monitoring procedures degenerate to a binary quantity. To guarantee a feasible monitoring procedure, the head start has to be chosen proportional to the smoothing parameter and the control statistics have to be modified when used with the asymptotic variance. This result underlines the weakness of schemes with a fixed head start and of schemes based on the asymptotic variance if the smoothing parameter is small. The assumptions on the target process are very weak, and are usually satisfied for stationary processes. In addition, the asymptotic equivalence of the EWMA schemes and of repeated significance tests is shown.

A new multivariate EWMA control chart via multiple testing

This paper proposes a new type of multivariate EWMA control chart for detecting the process mean shift on the basis of a series of most recent T-squared statistics. We established a multiple hypothesis testing which uses the false discovery rate as the error to be controlled. Particularly, Benjamini–Hochberg procedure is applied to develop a new control scheme. A nonparametric density estimation based on the Parzen windows is adopted to approximate the distribution of the T-square statistics, from which the p-values are calculated. The performance of the proposed control charts is evaluated in terms of the out-of-control average run length and the in-control average run length according to various non-centrality parameters associated with the mean shifts. The result shows that the proposed control chart performs better than the existing multivariate EWMA chart for all mean shifts. The proposed method seems to be rigorous in the sense that error rates for the multiple hypotheses are considered in an integrated way via FDR rather than considering type I and II errors separately.

The Enhanced EWMA Control Chart with Autocorrelation

Control charts are effective tool with regard to improving process quality and productivity, Shewhart control charts are efficiently good at detecting large shifts in a given process but very slow in detecting small and moderate shifts, such problem could be tackled through design of sensitizing rules. It has been observed that autocorrelation has an advert effect on the control charts developed under the independence assumption [1]. In this article a new EWMA control chart has been introduced with autocorrelation and some run rule schemes were introduced to enhanced the performance of the EWMA control chart when autocorrelated. The three-out-of three EWMA scheme and three-out-of- four EWMA schemes were introduced and the generated data with induced autocorrelation were used to construct the EWMA chart to sensitize the shifts presence. Simulation of autocorrelated data were carried out for the proposed schemes which detects the shifts as soon as it occurs in the given process, the performance were evaluated using the ARL (average run length) and the results were compared with the published results of Steiner (1991) and the Saccucci (1990) which were designed for large, small and moderate shift. The results indicates that the proposed schemes are more sensitive to the shifts at ARL0=500, 300 and 200 with autocorrelation of 0.2, 0.5 and 0.9 considered in the study.

USAGE OF CONTROL CHARTS FOR TIME SERIES ANALYSIS IN FINANCIAL MANAGEMENT

We will deal with corporate financial proceeding using statistical process control, specifically time series control charts. The article outlines intersection of two disciplines, namely econometrics and statistical process control. Theoretical part discusses methodology of time series control charts, and in research part, the methodology is demonstrated on two case studies. The first focuses on analysis of Slovak currency from the perspective of its usefulness for generating profits through time series control charts. The second involves regulation of financial flows for a heteroskedastic financial process by EWMA and ARIMA control charts. We use Box-Jenkins methodology to find models of time series of annual Argentinian Gross Domestic Product available as a basic index from 1951–1998. We demonstrate the versatility of control charts not only in manufacturing but also in managing financial stability of cash flows. Specifically, we show their sensitivity in detecting even small shifts in mean which may indicate financial instability. This analytical approach is widely applicable and therefore of theoretical and practical interest.

Monitoring analytical measurements in presence of two component measurement error

Control charts are increasingly adopted by laboratories for effective monitoring of analytical processes. Analytical methods are mostly subject to two types of measurement errors, i—additive and ii—multiplicative, or proportional, error. These errors have been combined in a single model, namely the two component error model (TCME) proposed by [1]. In this study we present a comparison among the performance of three widely used location control charts, i.e. Shewhart, CUSUM and EWMA charts in presence of TCME model. This study will help quality practitioners to choose an efficient chart for the monitoring of analytical measurements.

Economic-Statistical Design of EWMA Control Charts Based on Taguchi's Loss Function

This paper proposes an economic-statistical design of the EWMA chart with time-varying control limits in which the Taguchi's quadratic loss function is incorporated into the economic-statistical design based on Lorenzen and Vance's economical model. A nonlinear programming with statistical performance constraints is developed and solved to minimize the expected total quality cost per unit time. This model, which is divided into three parts, depends on whether production continues during the period when the assignable cause is being searched for and/or repaired. Through a computational procedure, the optimal decision variables, including the sample size, the sampling interval, the control limit width, and the smoothing constant, can be solved for by each model. It is showed that the optimal economic-statistical design solution can be found from the set of optimal solutions obtained from the statistical design, and both the optimal sample size and sampling interval always decrease as the magnitude of shift increases.

Quality surveillance with EWMA control charts based on exact control limits

The control charts are main tools of statistical surveillance of quality in production processes. Exponentially weighted moving average charts that make use of exact control limits are discussed in detail in this paper. We start by assessing the impact of the smoothing constant \(\lambda \) not only in the in-control average run length (ARL) of upper one-sided EWMA charts with exact control limits, but also in the range of the exact control limits of such charts with a common in-control ARL value (i.e. matched in-control). Based on the analytical results and on an extensive simulation study we conclude that the out-of-control ARL of matched in-control upper one-sided EWMA charts with exact control limits increases with \(\lambda \). This in turn suggests the use of \(\lambda \) values as close to the zero as possible and motivates what we called the (upper one-sided) limit chart. Its performance is extensively studied with regard to the ARL. Finally, we investigate the impact of \(\lambda \) on the ARL of EWMA charts with asymptotic control limits; the (maximum) conditional average delay is also addressed as an additional performance measure.

Construction of control charts by using Fuzzy Multinomial -FM and EWMA Chart “Comparative study"

The control chart is a graphical tool for monitoring the activities of a manufacturing process.
 It plays a vital role in Statistical Process Control (SPC). These charts help us to take correct
 decisions. The use of statistical methods in statistical quality control has a long history. The P-
 chart plays the important role in controlling the fraction of nonconforming article produced.
 The use of fuzzy has an effective role with inaccurate data. Great efforts have been made in the
 direction of combining the Quality Control with fuzzy concept. Therefore; Fuzzy control chart
 are connecting link between fuzzy logic and Quality Control technique, the goal of this
 connection is to combine the advantage of both disciplines in order to process deal with linguistic
 concepts and classified each item in more than two categories such as bad, medium, good, very
 good and excellent.
 This paper presents an extension of standard control chart to deal with linguistic categories
 and the variable sampling size (VSS), it is named as fuzzy multinomial charts (FM-chart), and
 we illustrate this approach by numerical example. This paper is comparing FM-chart with the
 conventional p – chart and EWMA Control Chart. It is seen that FM chart with VSS performs
 better than the conventional charts, this method is more sensitive, accurate and more economic
 for assisting decision maker to control the operation system as early time, especially when there
 is a change in sample sizes.

An optimization design of the 3-EWMA scheme for monitoring mean shifts

This article presents an algorithm for the optimization design of the three exponentially weighted moving average control chart scheme (3-EWMA scheme in short) for monitoring a range of mean shifts. The design algorithm optimizes the charting parameters of the 3-EWMA scheme, based on extra quadratic loss function. The results of comparative studies and an example show that the optimal 3-EWMA scheme always outperforms the basic 3-EWMA scheme, as well as the other EWMA charts under different specifications. According to a 2k factorial experiment, the optimal 3-EWMA scheme outperforms the main competitor, the basic 3-EWMA scheme, by more than 15 %, on average. Although the design of the optimal 3-EWMA scheme is more difficult than that of the conventional EWMA charts, it can be easily computerized. Moreover, this article provides the statistical process control (SPC) practitioners with a design table to facilitate the designs of the 3-EWMA schemes. From this design table, the users can directly find the optimal values of the charting parameters according to the design specifications. In general, this article will help to enhance the detection effectiveness of the 3-EWMA scheme, and facilitate its applications in SPC.

Comparing Robustness of EWMA Dispersion Control Chart for Non-Normal Process

This article discusses robustness to non-normality of EWMA charts for dispersion. Comparison analysis of run length of four kinds of EWMA charts to monitoring process dispersion is provided to evaluate control charts performance and robustness. At last robust EWMA dispersion charts for non-normal processes are proposed by this way.

Application of Multivariate Process Control (MPC) in the Natural Rubber Industry

Statistical process control (SPC) monitors specified quality characteristics of a product orservice to detect whether the process has changed in a way that would affect product qualityand to measure the current quality of products or services. This study introduces severalapplications on multivariate process control in the rubber industry employing the factory datain the Dartonfield estate of the Rubber Research Institute of Sri Lanka (RRI). Multivariateprocess control was applied to consider two or more variables simultaneously. In this studymultivariate techniques were done for the application of bleaching agents, sodium bisulphateand acids in the process of crepe rubber production.Multivariable scatter diagrams and control ellipse has been used to show the process whenthe multivariate data composed of two variables. Hotelling T2 control chart was used tomonitor application of chemicals simultaneously in a single chart. Principal components wereused to interpret dimensions of components and star charts were applied to diagnostic fordetermining the relative contributions of the each chemical component. The multivariateEWMA (MEWMA) control chart for monitoring the process mean vector was astraightforward extension of the univariate EWMA chart. The graphical presentation is veryimportant and it is a quick way to see the advantages of MPC.Multivariate Statistical analysis is concerned with data that consist of sets of measurementson a number of variables. So, multivariate quality control provides a way for monitoring andevaluation of chemical application process. Scatter plots and control ellipse is very importantto detect out of control points and relationships as a graphical method. Hotelling T2 is animportant chart that can be decomposed into an overall measure of distance of the groupmeans from the target T2 and measure of variability. Principal components can be useful formultivariate quality control, especially to observe variation of dimensions of chemicalapplications. Multivariate EWMA procedure use additional information from recent historyof the process and it is more sensitive in monitoring chemical application process.Therefore multivariate process control provides way for manufacturer to test their products inan environment that provide many advantages over univariate models.

Enhancing the Performance of Exponentially Weighted Moving Average Charts: Discussion

Abbas et al. (Abbas N, Riaz M, Does RJMM. Enhancing the performance of EWMA charts. Quality and Reliability Engineering International 2011; 27(6):821–833) proposed the use of signaling schemes with exponentially weighted moving average charts (named as 2/2 and modified − 2/3 schemes) for their improved design structures. A two‐sided control structure of these schemes is given in the paper. The computational results in some of the tables of that paper for modified − 2/3 are mistakenly given for the one‐sided control structure. The corrected two‐sided results are provided here. It is noticed that the superiority of the proposed scheme over the classical exponentially weighted moving average chart remains but is less pronounced. Copyright © 2014 John Wiley & Sons, Ltd.

Guidelines for Applying Statistical Quality Control Method to Monitor Autocorrelated Prcoesses

The implementation of statistical control charts under autocorrelated situations is a critical issue since it has a significant impact on the monitoring capability of manufacturing processes. The objective of this study is to assess the performance of control charts under different scenarios and to optimize the design of control charts to best deal with autocorrelated processes. To achieve the proposed objective, two autoregressive integrated moving average models, ARIMA (1, 0, 1) and ARIMA (0, 1, 1), are utilized to characterize stationary and non-stationary processes. These process models were simulated to achieve the response, average run length (ARL), which is the performance measure of this study. The factorial design of experiment was conducted to quantify the effect of critical factors, i.e., ARIMA coefficients, types of charts (exponentially weighted moving average: EWMA and moving range: MR) and shift sizes on the ARL. The experimental results show that EWMA chart is the most appropriate control chart to monitor autocorrelated observations. Additionally, both AR and MA parameters along with shift sizes have a significant effect on the performance of control charts. Therefore, this study has pointed out a suitable tool for use under the different scenarios of autocorrelation. The validation of the above experimental results was conducted on another ARIMA model, ARIMA (1, 0, 0). If the performance of control charts under autocorrelated disturbances is correctly characterized, practitioners will have guidelines for achieving the highest possible performance potential when deploying SPC.

Statistical surveillance of the mean vector and the covariance matrix of nonlinear time series

The purpose of this paper is to jointly monitor the mean vector and the covariance matrix of multivariate nonlinear times series. The underlying target process is assumed to be a constant conditional correlation process Bollerslev (Rev Econ Stat 72:498–505, 1990) or a dynamic conditional correlation model Engle (J Bus Econ Stat 20:339–350, 2002). We introduce several EWMA and CUSUM control charts. These control schemes are based on univariate EWMA statistics, multivariate EWMA recursions, and different types of cumulative sums. The recursions are applied to local measures for means and covariances, e.g. the present observations and the conditional covariances. Further, they are applied to means and covariances of residuals. The control statistics are obtained by computing the Mahalanobis distance between the EWMA or CUSUM statistics and their expectations if no change occurs. Via Monte Carlo simulation the performance of the proposed charts is compared. Our empirical study illustrates an application of these control procedures to bivariate logarithmic returns of the European indices FTSE100 and DAX. In order to assess the performance of the introduced schemes we apply the average run length and the maximum conditional expected delay.

EWMA p charts under sampling by variables

When it comes to manufacturing processes, the question of process quality is omnipresent. Statistical methods for monitoring quality measures are widespread and control charts are well established. Instead of checking parameters such as and , there are control charts to monitor the percent defective . While control charts under sampling by attributes are already illustrated in the literature, this paper develops and modifies different approaches of control charts for under sampling by variables. The results for a modified exponentially moving average chart, EWMA , are compared to those of several control charts. The new scheme is well suited for imperfect in-control situations, that is, the pre-run sample mean differs from a certain natural or target mean value of the monitored parameter. To calculate the most popular control chart performance measure, the average run length (), both the Markov chain approach and the collocation method are used. It turns out that the EWMA chart has properties similar to the usual EWMA and the CUSUM charts. Thus, it can be a helpful utility for practical applications.

Effect of Resolution of Measurements in the Behavior of Exponentially Weighted Moving Average Control Charts

Process behavior is known through measurement. All measurements are discrete and transform a continuous process distribution into a discrete (multinomial) measurement distribution. In this article, properties of exponentially weighted moving average control charts (EWMA charts) of measurements are studied through Monte Carlo simulations. Detection capabilities (average run length curves) are presented as a function of measurement resolution and recommendations for proper design of a measuring system are given. EWMA charts measurement resolution requirements are compared to Shewhart charts, and two examples are presented to illustrate behavior differences. Industry performs quality control activities in order to control raw materials, processes, and finished products with the purpose of delivering products to market complying with quality requirements. Different statistical methods are used in chemical, physical, and biological analysis and nearly all control methods will use measurement devices. Quality control is mandatory for many industries, for example, the pharmaceutical industry, and it is a very costly activity. The selection of suitable methods of control and appropriate measurement devices acquire special relevance for obtaining efficient results. Measurement devices require a certain measurement capability and must be fit for the purpose of controlling the quality of processes and products. The equipment capability includes, among other elements, the resolution, which means the "smallest change in a quantity being measured that causes a perceptible change in the corresponding indication". Different control charts have been extensively used for statistical process control. Based on cases from the pharmaceutical industry and simulation tools, this paper studies the influence of resolution of measurement devices in exponentially weighted moving average control charts (EWMA charts). In addition, a comparison of EWMA charts and traditional Shewhart charts is presented in order to offer support to the practitioners.