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Testing the equality of two independent normal populations is a perfect case of the two-sample problem, yet it is not treated in the main text of any textbook or handbook. In this article, we derive the exact distribution of the likelihood ratio test and implement this test with an R function. This article has supplementary materials online.

The authors derive the analytic expressions for the mean and variance of the log-likelihood ratio for testing equality of k (k ≥ 2) normal populations, and suggest a chi-square approximation and a gamma approximation to the exact null distribution. Numerical comparisons show that the two approximations and the original beta approximation of Neyman and Pearson (1931) are all accurate, and the gamma approximation is the most accurate.

After pointing out a drawback in Bartlett's chi-square approximation, we suggest a simple modification and a Gamma approximation to improve Bartlett's M test for homogeneity of variances.

In this article, we propose an empirical likelihood-based test to check the existence of serial correlation in partial linear errors-in-variables models. A nonparametric version of Wilk' theorem is derived, which says that our proposed test has an asymptotic chi-square distribution. Simulation results reveal that the finite sample performance of our proposed test is satisfactory in both size and power.

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.

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.

Lower-sided and upper-sided exponentially weighted moving average (EWMA) charts are developed for detecting mean changes when censoring occurs at a fixed level in processes characterized by Weibull distributions. The lower-sided EWMA chart performs bett..

The MaxEWMA chart has recently been introduced as an alternative to control charting procedures that are designed to jointly detect changes in the mean and standard deviation of a normally distributed process. Here, a method for computing both in-control and out-of-control average run lengths for purposes of effectively designing this chart is offered. Design strategies are considered, numerical results to aid the design effort are given, and examples are discussed.

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.

It is known that due to the existence of the nonparametric component, the usual estimators for the parametric component or its function in partially linear regression models are biased. Sometimes this bias is severe. To reduce the bias, we propose two jackknife estimators and compare them with the naive estimator. All three estimators are shown to be asymptotically equivalent and asymptotically normally distributed under some regularity conditions. However, through simulation we demonstrate that the jackknife estimators perform better than the naive estimator in terms of bias when the sample size is small to moderate. To make our results more useful, we also construct consistent estimators of the asymptotic variance, which are robust against heterogeneity of the error variances.

We prove that the standard EWMA mean chart with asymptotic control limits and the EWMA mean chart with time-varying control limits for monitoring mean changes in a normal process with known mean and known variance are ARL-unbiased. Using the results derived we discuss the effects of estimation of the process mean on ARL.

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...

We give simple and concise expressions of influence measures for general linear models with correlated errors. We show that the commonly used influence measures can be expressed as functions of the generalized leverages and residuals and have the same forms as those in standard linear regression models.

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..

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..

The importance of the independence between a standard normal and a chi-square random variable in constructing a t random variable is explored. When independence is absent it is demonstrated that the usual t approximation can lead to misleading results.