Exponentially Weighted Research Articles

Two formulations of exponentially weighted enhanced LQ controllers

Properties of a class of multiinput multioutput digital controllers are examined. The controllers incorporate three features: (1) optimal gains associated with known exogenous inputs; (2) penalties imposed both on squares of first backward differences in control actions and on control actions squared; and (3) exponential weighting to ensure bounds on closed-loop eigenvalues. Two versions of exponential weighting are treated. Results are given for both the finite-horizon and infinite-horizon versions of the problems. The results include expressions for optimal feedback gains and for optimal preview gains. For the infinite-horizon versions, relationships are derived between the optimal closed-loop eigenvalues and the eigenvalues associated with the preview gains. Two examples are given to illustrate properties of three controllers. >

Control Charts in the Presence of Data Correlation

Traditional statistical process control charts assume that observations are independent and normally distributed about some mean. We investigate the robustness of traditional charts to data correlation when the correlation can be described by an ARMA(1,1) model. We compare the performance of the Shewhart chart and the Exponentially Weighted Moving Average (EWMA) chart to the performance of the Special-Cause Control (SCC) chart and the Common-Cause Control (CCC) chart proposed by Alwan and Roberts (1988), which are designed to account for data correlation. We also explore the possibility of putting limits on the CCC chart, in order to predict quality abnormalities. The measure of performance used is the average run length (ARL). The results show that the ability of the EWMA chart to detect shifts in the process mean is quite robust to data correlation, while the corresponding individuals Shewhart chart rarely detects such shifts more quickly than the other charts. The SCC and CCC charts are shown to be preferred in most cases when a shift in the process mean exceeds 2 standard deviations. The experimental results can aid practitioners in deciding which chart would be most effective at detecting specified shifts in the process mean given the nature of their particular correlated environments. Two methodologies are utilized to explain the relative performance of the SPC charts compared: the dynamic step response function, and response surface methodology. Such methods not only facilitate a discussion of our results, but also make it possible to predict the relative performance of the charts when the process can be described by a model which is more complex than the ARMA(1,1) model.

Pointwise Exponentially Weighted Estimates for Approximation on the Half-Line

We establish a theorem in the style of Timan-Gopengauz which provides pointwise estimates for the simultaneous approximation of a function and its derivatives in the space C[0, ∞), with error measured in an exponentially weighted norm.

Some Omnibus Exponentially Weighted Moving Average Statistical Process Monitoring Schemes

Exponentially weighted moving average (EWMA) quality-monitoring schemes capahlc of detecting changes in both location and spread, referred to as omnibus EWMA's. are proposed. Omnibus EWMA's are based on the exponentiation of the absolute value of the standardized sample mean of the observations. The process target mean and standard deviation are used for standardizing. Design procedures and considerations, including a fast initial response feature, are discussed. Average run lengths for exponents of .5 and 2 and various values of the weighting constant are presented. The proposed schemes are compared with each other and with a number of selected, well-known omnibus schemes and a proposed omnibus cumulative sum scheme. Schemes with different sample sizes are used, and off-target models include both static and dynamic alternatives. Comparisons are based on average number of observations to detection and expected loss due to poor quality. One of the omnibus EWMA schemes is shown to be best with regard to exp...

Some Omnibus Exponentially Weighted Moving Average Statistical Process Monitoring Schemes

Exponentially weighted moving average (EWMA) quality-monitoring schemes capahlc of detecting changes in both location and spread, referred to as omnibus EWMA's. are proposed. Omnibus EWMA's are based on the exponentiation of the absolute value of the standardized sample mean of the observations. The process target mean and standard deviation are used for standardizing. Design procedures and considerations, including a fast initial response feature, are discussed. Average run lengths for exponents of .5 and 2 and various values of the weighting constant are presented. The proposed schemes are compared with each other and with a number of selected, well-known omnibus schemes and a proposed omnibus cumulative sum scheme. Schemes with different sample sizes are used, and off-target models include both static and dynamic alternatives. Comparisons are based on average number of observations to detection and expected loss due to poor quality. One of the omnibus EWMA schemes is shown to be best with regard to exp...

Direct model reference adaptive pole placement control with exponential weighting properties

A parameterization for a linear system is presented to design a direct model reference adaptive pole placement controller. This parameterized model is one of the structured nonminimal models. The exponentially weighted least-squares algorithm is employed to estimate the control parameters. The direct adaptive controller has the exponential weighting properties by the proposed method of selecting the characteristic polynomials of the sensitivity function filters in connection with the reference model. >

Target zone exchange rate

This paper attempts to rationalize the target zone exchange rate system's width proposed by Williamson (1983). The model is a special case of the Exponentially Weighted Moving Average (EWMA) function. Given the time series distribution, estimated means and variances are plotted on a bounded (upper and lower) standard normal distribution.

Development and Evaluation of Control Charts Using Exponentially Weighted Moving Averages

Some studies have been done to construct quality control charts using the Exponentially Weighted Moving Average, EWMA. However, they have been done implicitly for subgroups of size n and individual data. Moreover, the emphasis of the control chart of ..

Discrete adaptive observer with exponential weighting properties

An adaptive observer based on the exponentially weighted least-squares method is studied, and a method of selecting the state variable filters is proposed. By this method, all the past measurement data are weighted exponentially both with weighting coefficient and the state variable filters. The proposed scheme guarantees fast convergence and is very stable.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The Exponentially Weighted Moving Average

The Shewhart and CUSUM control chart techniques have found wide application in the manufacturing industries. However, workpiece quality has also been greatly enhanced by rapid and precise individual item measurements and by improvements in automatic dynamic machine control. One consequence is a growing similarity in the control problems faced by the workpiece quality control engineer and his compatriot in the continuous process industries. The purpose of this paper is to exposit a control chart technique that may be of value to both manufacturing and continuous process quality control engineers: the exponentially weighted moving average (EWMA) control chart. The EWMA has its origins in the early work of econometricians, and although its use in quality control has been recognized, it remains a largely neglected tool. The EWMA chart is easy to plot, easy to interpret, and its control limits are easy to obtain. Further, the EWMA leads naturally to an empirical dynamic control equation.

An Efficiency Property of the Exponentially Weighted Least Squares Estimators

An Efficiency Property of the Exponentially Weighted Least Squares Estimators

Comparison of Different Systems of Exponentially Weighted Prediction

Comparison of Different Systems of Exponentially Weighted Prediction