Cause-selecting charting techniques in multistage processes

Most of the products produced today are the results of several process stages. With the emphasis in industry on improved quality, control charts are widely used for process monitoring. However, conventional SPC techniques focus mostly on individual stages in a process and do not consider disseminating information throughout the multiple stages of the process. They are shown to be ineff'ective in analyzing multistage processes. A different approach to this problem is the cause-selecting chart (CSC), proposed by Zhang (1980, 1982, 1984, 1985a, 1985b, 1989a, 1989b, 1992). The CSC based on the output adjusted for the effect of the incoming quality shows promise for increasing the ability to analyze multistage processes. It starts a new field of control charting and much more work is required on this subject. In practice, the model relating input and output measures often needs to be estimated before the CSC is implemented. Little is known about the performance of the CSC when the model parameters are estimated. In this thesis, the effect of parameter estimation is investigated. To get a better understanding of the performance of CSCs with estimated parameters, their run-length distributions are analytically derived. A numerical procedure based on Gaussian quadrature is used to evaluate the run-length distribution. The simple linear regression model widely discussed in the CSC is insufficient to capture the stochastic behavior of the output. Taking the process dynamics and the autocorrelation structure of the disturbance into account, a more realistic CSC model is described. Like the conventional residual-based charting methods, the autocorrelation is removed by filtering the output with an inverse filter. However, by doing so, the resulting mean shift in the residual is varying over time, which has been referred to as the fault signature. In an attempt to make use of the valuable information contained in the fault signature, the cumulative score (Cuscore) chart and the triggered Cuscore chart are proposed. It is shown that the triggered Cuscore chart performs better than the standard Cuscore chart and the residual-based CUSUM chart. The multiple CSC (MCSC) is more adaptable than the CSC, which deals with the case with multiple uncontrollable assignable causes. The design and implementation of the MCSC is discussed in this thesis when the model parameters are estimated. Two estimation procedures are considered: the least squares estimation and principal components regression (PCR). It is shown that using prediction limits is quite effective in terms of maintaining a desired false-alarm rate under both procedures. It is expected that this research will greatly expand the scope of Conventional quality research

Exponentially weighted moving average control charts for monitoring increases in Poisson rate

The Exponentially Weighted Moving Average (EWMA) control chart has been widely studied as a tool for monitoring normal processes due to its simplicity and efficiency. However, relatively little attention has been paid to EWMA charts for monitoring Poisson processes. This article extends EWMA charts to Poisson processes with an emphasis on quick detection of increases in Poisson rate. Both cases with and without normalizing transformation for Poisson data are considered. A Markov chain model is established to analyze and design the proposed chart. A comparison of the results obtained indicates that the EWMA chart based on normalized data is nearly optimal

An Adaptive CUSUM Procedure for Signaling Process Variance Changes of Unknown Sizes

Similar to the CUSUM location chart, the traditional CUSUM dispersion chart can be designed to optimize the detection of specified variance changes. However, this optimality property requires that the magnitude of the out-of-control variance is known exactly a priori. To get away from this requirement, this paper suggests an adaptive CUSUM procedure for signaling changes in the process variance of unknown sizes. The basic idea is to first estimate the current process variance and then dynamically adjust the CUSUM chart to match the variance estimate. A two-dimensional Markov chain model is developed to analyze the chart performance. The comparison results with the traditional CUSUM dispersion chart and other competitive procedures favor the proposed one

Adaptive EWMA procedures for monitoring processes subject to linear drifts

The conventional Statistical Process Control (SPC) techniques have been focused mostly on the detection of step changes in process means. However, there are often settings for monitoring linear drifts in process means, e.g., the gradual change due to tool wear or similar causes. The adaptive exponentially weighted moving average (AEWMA) procedures proposed by Yashchin (1995) have received a great deal of attention mainly for estimating and monitoring step mean shifts. This paper analyzes the performance of AEWMA schemes in signaling linear drifts. A numerical procedure based on the integral equation approach is presented for computing the average run length (ARL) of AEWMA charts under linear drifts in the mean. The comparison results favor the AEWMA chart under linear drifts. Some guidelines for designing AEWMA charts for detecting linear drifts are presented.Average run length Integral equation Linear trend Statistical Process Control Exponentially weighted moving average

Bivariate Continuous Negatively Correlated Proportional Models with Applications in Schizophrenia Research

Bivariate continuous negatively correlated proportional data defined in the unit square (0,1)2 often appear in many different disciplines, such as medical studies, clinical trials and so on. To model this type of data, the paper proposes two new bivariate continuous distributions (i.e., negatively correlated proportional inverse Gaussian (NPIG) and negatively correlated proportional gamma (NPGA) distributions) for the first time and provides corresponding distributional properties. Two mean regression models are further developed for data with covariates. The normalized expectation–maximization (N-EM) algorithm and the gradient descent algorithm are combined to obtain the maximum likelihood estimates of parameters of interest. Simulations studies are conducted, and a data set of cortical thickness for schizophrenia is used to illustrate the proposed methods. According to our analysis between patients and controls of cortical thickness in typical mutual inhibitory brain regions, we verified the compensatory of cortical thickness in patients with schizophrenia and found its negative correlation with age

Bivariate Continuous Negatively Correlated Proportional Models with Applications in Schizophrenia Research

Bivariate continuous negatively correlated proportional data defined in the unit square (0,1)2 often appear in many different disciplines, such as medical studies, clinical trials and so on. To model this type of data, the paper proposes two new bivariate continuous distributions (i.e., negatively correlated proportional inverse Gaussian (NPIG) and negatively correlated proportional gamma (NPGA) distributions) for the first time and provides corresponding distributional properties. Two mean regression models are further developed for data with covariates. The normalized expectation–maximization (N-EM) algorithm and the gradient descent algorithm are combined to obtain the maximum likelihood estimates of parameters of interest. Simulations studies are conducted, and a data set of cortical thickness for schizophrenia is used to illustrate the proposed methods. According to our analysis between patients and controls of cortical thickness in typical mutual inhibitory brain regions, we verified the compensatory of cortical thickness in patients with schizophrenia and found its negative correlation with age

An np control chart for monitoring the mean of a variable based on an attribute inspection

This article proposes a new np control chart, called the npx chart, that employs an attribute inspection (inspecting whether a unit is conforming or nonconforming) to monitor the mean value of a variable x. The distinctive feature of the npx chart is using the statistical warning limits to replace the specification limits for the classification of conforming or nonconforming units. By optimizing the warning limits, the npx chart usually outperforms the X¯ chart on the basis of same inspection cost. In addition, the npx chart often works as a leading indicator of trouble and allows operators to take corrective action before any defective is actually produced.Quality control Statistical process control Attribute and variable control charts Attribute inspection Average time to signal Loss function