Using p values to design statistical process control charts

Conventional Phase II statistical process control (SPC) charts are designed using control limits; a chart gives a signal of process distributional shift when its charting statistic exceeds a properly chosen control limit. To do so, we only know whether a chart is out-of-control at a given time. It is therefore not informative enough about the likelihood of a potential distributional shift. In this paper, we suggest designing the SPC charts using p values. By this approach, at each time point of Phase II process monitoring, the p value of the observed charting statistic is computed, under the assumption that the process is in-control. If the p value is less than a pre-specified significance level, then a signal of distributional shift is delivered. This p value approach has several benefits, compared to the conventional design using control limits. First, after a signal of distributional shift is delivered, we could know how strong the signal is. Second, even when the p value at a given time point is larger than the significance level, it still provides us useful information about how stable the process performs at that time point. The second benefit is especially useful when we adopt a variable sampling scheme, by which the sampling time can be longer when we have more evidence that the process runs stably, supported by a larger p value. To demonstrate the p value approach, we consider univariate process monitoring by cumulative sum control charts in various cases.     

Reducing component estimation for varying coefficient models

The estimation problem for varying coefficient models has been studied by many authors. We consider the problem in the case that the unknown functions admit different degrees of smoothness. In this paper we propose a reducing component local polynomial method to estimate the unknown functions. It is shown that all of our estimators achieve the optimal convergence rates. The asymptotic distributions of our estimators are also derived. The established asymptotic results and the simulation results show that our estimators outperform the the existing two-step estimators when the coefficient functions admit different degrees of smoothness. We also develop methods to speed up the estimation of the model and the selection of the bandwidths.     

Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications

In this paper, the Rosenthal-type maximal inequalities and Kolmogorov-type exponential inequality for negatively superadditive-dependent (NSD) random variables are presented. By using these inequalities, we study the complete convergence for arrays of rowwise NSD random variables. As applications, the Baum–Katz-type result for arrays of rowwise NSD random variables and the complete consistency for the estimator of nonparametric regression model based on NSD errors are obtained. Our results extend and improve the corresponding ones of Chen et al. [On complete convergence for arrays of rowwise negatively associated random variables. Theory Probab Appl. 2007;52(2):393–397] for arrays of rowwise negatively associated random variables to the case of arrays of rowwise NSD random variables.     

Dirichlet Processes in Nonlinear Mixed Effects Models

In this article, we use two efficient approaches to deal with the difficulty in computing the intractable integrals when implementing Gibbs sampling in the nonlinear mixed effects model (NLMM) based on Dirichlet processes (DP). In the first approach, we compute the Laplace's approximation to the integral for its high accuracy, low cost, and ease of implementation. The second approach uses the no-gaps algorithm of MacEachern and Müller (1998 MacEachern , S. , Müller , P. ( 1998 ). Estimating mixtures of Dirichlet process models . Journal of Computational and Graphical Statistics 7 : 223 – 238 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) to perform Gibbs sampling without evaluating the difficult integral. We apply both approaches to real problems and simulations. Results show that both approaches perform well in density estimation and prediction and are superior to the parametric analysis in that they can detect important model features, such as skewness, long tails, and multimodality, whereas the parametric analysis cannot.     

A simulation study of ridge and other regression estimators

We consider a number of estimators of regression coefficients, all of generalized ridge, or 'shrinkage' type. Results of a simulation study indicate that with respect to two commonly used mean square error criteria, two ordinary ridge estimators, one proposed by Hoerl, Kennard and Baldwin, and the other introduced here, perform substantially better than both least squares and the other estimators discussed here     

Change-Point Estimation in Long Memory Nonparametric Models with Applications

We consider the estimation of a change point or discontinuity in a regression function for random design model with long memory errors. We provide several change-point estimators and investigate the consistency of the estimators. Using the fractional ARIMA process as an example of long memory process, we report a small Monte Carlo experiment to compare the performance of the estimators in finite samples. We finish by applying the method to a climatological data example.     

Influence Diagnostics of Semiparametric Nonlinear Reproductive Dispersion Models

This article proposes a semiparametric nonlinear reproductive dispersion model (SNRDM) which is an extension of nonlinear reproductive dispersion model and semiparametric regression model. Maximum penalized likelihood estimators (MPLEs) of unknown parameters and nonparametric functions in SNRDMs are presented. Some novel diagnostic statistics such as Cook distance and difference deviance for parametric and nonparametric parts are developed to identify influence observations in SNRDMs on the basis of case-deletion method, and some formulae readily computed with the MPLEs algorithm for diagnostic measures are given. The equivalency of case-deletion models and mean-shift outlier models in SNRDM is investigated. A simulation study and a real example are used to illustrate the proposed diagnostic measures.     

A Weighting Approach for GEE Analysis with Missing Data

We propose a new weighting (WT) method to handle missing categorical outcomes in longitudinal data analysis using generalized estimating equations (GEE). The proposed WT provides a valid GEE estimator when the data are missing at random (MAR), and has more stable weights and shows advantage in efficiency compared to the inverse probability weighing method in the presence of small observation probabilities. The WT estimator is similar to the stabilized weighting (SWT) estimator under mild conditions, but it is more stable and efficient than SWT when the associations of the outcome with the observation probabilities and the covariate are strong.     

An Extension of Economic Design of x-Bar Control Charts for Non Normally Distributed Data Under Weibull Shock Models

Three parameters—sample size, sampling intervals, and the control limits—must be determined when the x bar chart to monitor a manufacturing process. The constant sampling intervals were widely employed because of its administrative simplicity. However, the variable sampling interval (VSI) has recently been shown to give substantially faster detection of most process shifts than fixed-sampling-interval (FSI) for x-bar charts. In addition, these measurements in the subgroup are assumed to be normally distributed. That assumption may not be tenable. This investigation compares the economic design of x-bar control charts for non normal data under Weibull shock models with various sampling avenues.     

An Application of Matrix Power Series to Linear Models

In the system of two seemingly unrelated regressions, employing a matrix power series, we show that the two-stage estimator is better than the ordinary least square estimator (OLSE) in terms of the mean square error matrix (MSEM) criterion. The result enriches the existing literature and can be applied to many fields of applications related to economics and statistics.