Gemai Chen

A General Purpose Approximate Goodness-of-Fit Test

Skewed distributions play an important role in the analysis of data from quality and reliability experiments. Very often unknown parameters must be estimated from the sample data in order to test whether the data has come from a certain family of distri..

Monitoring Process Mean and Variability With One EWMA Chart

Two EWMA charts are usually required to monitor both process mean and variability. In this paper, we propose a new EWMA chart which effectively combines the usual two EWMA charts into one chart. In particular, the new EWMA chart has the property that it is effective in detecting both increases and decreases in mean and/or variability.

EWMA Charts for Monitoring the Mean of Censored Weibull Lifetimes

A lower-sided and an upper-sided exponentially weighted moving average (EWMA) chart for detecting mean changes (decreases and increases) in processes characterized by Weibull distributions are developed in this paper when censoring occurs at a fixed level. We show that the lower-sided EWMA chart performs better than its counterpart, the Shewhart-type; that a Shewhart-type chart is not appropriate to detect mean increases when the censoring rate is high; and that the upper-sided EWMA chart works well in detecting mean increases.

A New Multivariate Control Chart for Monitoring Both Location and Dispersion

ABSTRACT A multivariate exponentially weighted moving average single control chart is developed in this article. This chart is capable of monitoring simultaneously the process mean vector and the process covariance matrix. Our average run length comparison shows that this new chart performs better than the combination of the χ2 chart and the |S| chart when small changes in the process parameters are of interest.

A New EWMA Control Chart for Monitoring Both Location and Dispersion

Abstract A new control chart, which employs the exponentially weighted moving average (EWMA) technique, is proposed. The statistic for the chart defines the area below a straight line as the control region, which makes the charting procedure easier than the usual approach. This chart can effectively monitor the process mean and the increased process variability simultaneously, and can detect the source and the direction of a change easily.

THE EXACT RUN LENGTH DISTRIBUTION AND DESIGN OF THE S2 CHART WHEN THE IN-CONTROL VARIANCE IS ESTIMATED

When monitoring the process variability, it is a common practice that a Phase I data set is used to estimate the unknown in-control process standard deviation σ0 or variance to set up the control limits, then monitoring proceeds. Once the process is considered to be in-control, the estimated control limits are assumed as fixed. This practice ignores the effect of estimating the unknown in-control process variance . In this paper, we derive the exact run length distribution of the S2 control chart when the in-control process variance is estimated and find that m = 200 or more Phase I samples are needed to neglect the effect of using estimated control limits. New control limits when m is small are also derived.

On t and EWMA t charts for monitoring changes in the process mean

The performance of an X-bar chart is usually studied under the assumption that the process standard deviation is well estimated and does not change. This is, of course, not always the case in practice. We find that X-bar charts are not robust against errors in estimating the process standard deviation or changing standard deviation. In this paper we discuss the use of a t chart and an exponentially weighted moving average (EWMA) t chart to monitor the process mean. We determine the optimal control limits for the EWMA t chart and show that this chart has the desired robustness property. Copyright

An Extended EWMA Mean Chart

Abstract In this paper, we extend the exponentially weighted moving average (EWMA) technique to double exponentially weighted moving average (DEWMA) technique. We show that DEWMA mean charts perform better than EWMA mean charts in detecting small mean shifts ranging from 0.1 to 0.5 of the process standard deviation, and that the two types of charts perform similarly when mean shifts are larger than 0.5 standard deviation. The design of DEWMA mean charts is also discussed.

Box-Cox transformations in linear models: large sample theory and tests of normality

The authors provide a rigorous large sample theory for linear models whose response variable has been subjected to the Box-Cox transformation. They provide a continuous asymptotic approximation to the distribution of estimators of natural parameters of the model. They show, in particular, that the maximum likelihood estimator of the ratio of slope to residual standard deviation is consistent and relatively stable. The authors further show the importance for inference of normality of the errors and give tests for normality based on the estimated residuals. For non-normal errors, they give adjustments to the log-likelihood and to asymptotic standard errors.

An Improved p Chart Through Simple Adjustments

The p chart for monitoring the fraction, p, of nonconforming products requires very large sample sizes to achieve any power in detecting decreases in p, and the false alarm for probabilities differ considerably from the nomial normal values. Two alterna..