Petros E. Maravelakis

An EWMA chart for monitoring the process standard deviation when parameters are estimated

The EWMA chart for the standard deviation is a useful tool for monitoring the variability of a process quality characteristic. The performance of this chart is usually evaluated under the assumption of known parameters. However, in practice, process parameters are estimated from an in-control Phase I data set. A modified EWMA control chart is proposed for monitoring the standard deviation when the parameters are estimated. The Run Length properties of this chart are studied and its performance is evaluated by comparing it with the same chart but with process parameters assumed known.

The Variable Sample Size X¯ Chart with Estimated Parameters

The VSS chart, dedicated to the detection of small to moderate mean shifts in the process, has been investigated by several researchers under the assumption of known process parameters. In practice, the process parameters are rarely known and are usually estimated from an in-control Phase I data set. In this paper, we evaluate the (run length) performances of the VSS chart when the process parameters are estimated, we compare them in the case where the process parameters are assumed known and we propose specific optimal control chart parameters taking the number of Phase I samples into account.

The Performance of the MEWMA Control Chart When Parameters Are Estimated

In the present article, we study the effect of estimating the vector of means and variance-covariance matrix in the performance of the multivariate exponentially weighted moving average (MEWMA) control chart. We show through simulation that the performance of the MEWMA control chart is affected when the parameters are estimated compared to the known parameters case. We show also that larger number of Phase I samples are required to achieve the expected statistical performance of the MEWMA chart when smaller smoothing constants are used in designing it. Under some sampling scenarios, more than 2,500 samples are needed to estimate the unknown parameters to satisfy the intended statistical performance. The control limit that achieves the desired in control ARL when estimating the parameters is computed in several cases and formulas used to find approximately its values are given. Finally, an optimal design strategy for the MEWMA chart with estimated parameters is presented.

Measurement error effect on the CUSUM control chart

The performance of the cumulative sum (CUSUM) control chart for the mean when measurement error exists is investigated. It is shown that the CUSUM chart is greatly affected by the measurement error. A similar result holds for the case of the CUSUM chart for the mean with linearly increasing variance. In this paper, we consider multiple measurements to reduce the effect of measurement error on the charts performance. Finally, a comparison of the CUSUM and EWMA charts is presented and certain recommendations are given.

The performance of multivariate CUSUM control charts with estimated parameters

In this paper, we study the effect of estimating the vector of means and the variance–covariance matrix on the performance of two of the most widely used multivariate cumulative sum (CUSUM) control charts, the MCUSUM chart proposed by Crosier [Multivariate generalizations of cumulative sum quality-control schemes, Technometrics 30 (1988), pp. 291–303] and the MC1 chart proposed by Pignatiello and Runger [Comparisons of multivariate CUSUM charts, J. Qual. Technol. 22 (1990), pp. 173–186]. Using simulation, we investigate and compare the in-control and out-of-control performances of the competing charts in terms of the average run length measure. The in-control and out-of-control performances of the competing charts deteriorate significantly if the estimated parameters are used with control limits intended for known parameters, especially when only a few Phase I samples are used to estimate the parameters. We recommend the use of the MC1 chart over that of the MCUSUM chart if the parameters are estimated from a small number of Phase I samples.

The EWMA median chart with estimated parameters

ABSTRACT The usual practice in control charts is to assume that the chart parameters are known or can be accurately estimated from in-control historical samples and the data are free from outliers. Both of these assumptions are not realistic in practice: a control chart may involve the estimation of process parameters from a very limited number of samples and the data may contain some outliers. In order to overcome these issues, in this article, we develop an Exponentially Weighted Moving Average (EWMA) median chart with estimated parameters to monitor the mean value of a normal process. We study the run length properties of the proposed chart using a Markov Chain approach and the performance of the proposed chart is compared to the EWMA median chart with known parameters. Several tables for the design of the proposed chart are given in order to expedite the use of the chart by practitioners. An illustrative example is also given along with some recommendations about the minimum number of initial subgroups m for different sample sizes n that must be collected for the estimation of the parameters so that the proposed chart has identical performance as the chart with known parameters. From the results we deduce that (i) there is a large difference between the known and estimated parameters cases unless the initial number of subgroups m is large; and (ii) the difference between the known and estimated parameters cases can be reduced by using dedicated chart parameters.

A compound control chart for monitoring and controlling high quality processes

In the present article, we propose a new control chart for monitoring high quality processes. More specifically, we suggest declaring the monitored process out of control, by exploiting a compound rule couching on the number of conforming units observed between the (i−1)th and the ith nonconforming item and the number of conforming items observed between the (i−2)th and the ith nonconforming item. Our numerical experimentation demonstrates that the proposed control chart, in most of the cases, exhibits a better (or at least equivalent) performance than its competitors.

Run length properties of run rules EWMA chart using integral equations

Abstract The EWMA chart is a control chart that is able to quickly detect small to moderate shifts in the process mean. Runs rules is a popular technique in the area of control charts that are used to improve the performance of the standard Shewhart control chart for the mean. Recently, several researchers investigated the performance of EWMA type control charts incorporating runs rules using either simulation or Markov chains. As these methods only yield approximate results, in this paper, we present an exact approach based on integral equations for studying the run length performance of the EWMA control chart with runs rules.

A new memory-type monitoring technique for count data

A new control scheme with memory is proposed and studied.It can be used for monitoring count data of any type.Its theoretical properties can be exactly derived.It has an increased sensitivity in the detection of small and moderate shifts.It can be used for monitoring industrial and non-industrial processes. The monitoring of count data arise in several industrial applications in which quality characteristics cannot be measured on a continuous numerical scale. Usually, in such cases the interest is on the number of defects or nonconformities that are produced from a manufacturing process. In this work, a new control scheme with memory, suitable for monitoring discrete data, is proposed and studied. It only uses integer-valued weights in the recent as well as in the past observations, while the plotted statistic is also a positive integer. An appropriate Markov chain technique is used for the determination of the entire run-length distribution of the proposed chart. Also, practical guidelines and comparisons with other competitive schemes are provided, demonstrating an increased sensitivity in the detection of small magnitude shifts, especially the decreasing ones. Finally, the practical application of the proposed scheme is illustrated with two numerical examples.

The Effect of Methods for Handling Missing Values on the Performance of the MEWMA Control Chart

This article is concerned with the effect of the methods for handling missing values in multivariate control charts. We discuss the complete case, mean substitution, regression, stochastic regression, and the expectation–maximization algorithm methods for handling missing values. Estimates of mean vector and variance–covariance matrix from the treated data set are used to build the multivariate exponentially weighted moving average (MEWMA) control chart. Based on a Monte Carlo simulation study, the performance of each of the five methods is investigated in terms of its ability to obtain the nominal in-control and out-of-control average run length (ARL). We consider three sample sizes, five levels of the percentage of missing values, and three types of variable numbers. Our simulation results show that imputation methods produce better performance than case deletion methods. The regression-based imputation methods have the best overall performance among all the competing methods.