Monitoring process mean and variability with one non-central chi-square chart

Traditionally, an (X) over bar -chart is used to control the process mean and an R-chart to control the process variance. However, these charts are not sensitive to small changes in process parameters. A good alternative to these charts is the exponentially weighted moving average (EWMA) control chart for controlling the process mean and variability, which is very effective in detecting small process disturbances. In this paper, we propose a single chart that is based on the non-central chi-square statistic, which is more effective than the joint (X) over bar and R charts in detecting assignable cause(s) that change the process mean and/or increase variability. It is also shown that the EWMA control chart based on a non-central chi-square statistic is more effective in detecting both increases and decreases in mean and/or variability.

An adaptive chart for monitoring the process mean and variance

Traditionally, an (X) over bar chart is used to control the process mean and an R chart is used to control the process variance. However, these charts are not sensitive to small changes in the process parameters. The adaptive ($) over bar and R charts might be considered if the aim is to detect small disturbances. Due to the statistical character of the joint (X) over bar and R charts with fixed or adaptive parameters, they are not reliable in identifing the nature of the disturbance, whether it is one that shifts the process mean, increases the process variance, or leads to a combination of both effects. In practice, the speed with which the control charts detect process changes may be more important than their ability in identifying the nature of the change. Under these circumstances, it seems to be advantageous to consider a single chart, based on only one statistic, to simultaneously monitor the process mean and variance. In this paper, we propose the adaptive non-central chi-square statistic chart. This new chart is more effective than the adaptive (X) over bar and R charts in detecting disturbances that shift the process mean, increase the process variance, or lead to a combination of both effects. Copyright (c) 2006 John Wiley & Sons, Ltd.

Monitoring the process mean and variance using a synthetic control chart with two-stage testing

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A synthetic control chart for monitoring the process mean and variance

Purpose - The aim of this paper is to present a synthetic chart based on the non-central chi-square statistic that is operationally simpler and more effective than the joint X̄ and R chart in detecting assignable cause(s). This chart will assist in identifying which (mean or variance) changed due to the occurrence of the assignable causes. Design/methodology/approach - The approach used is based on the non-central chi-square statistic and the steady-state average run length (ARL) of the developed chart is evaluated using a Markov chain model. Findings - The proposed chart always detects process disturbances faster than the joint X̄ and R charts. The developed chart can monitor the process instead of looking at two charts separately. Originality/value - The most important advantage of using the proposed chart is that practitioners can monitor the process by looking at only one chart instead of looking at two charts separately. © Emerald Group Publishing Limted.

Synthetic control chart for monitoring the pprocess mean and variance

In this article, we consider the synthetic control chart with two-stage sampling (SyTS chart) to control the process mean and variance. During the first stage, one item of the sample is inspected; if its value X, is close to the target value of the process mean, then the sampling is interrupted. Otherwise, the sampling goes on to the second stage, where the remaining items are inspected and the statistic T = Sigma [x(i) - mu(0) + xi sigma(0)](2) is computed taking into account all items of the sample. The design parameter is function of X-1. When the statistic T is larger than a specified value, the sample is classified as nonconforming. According to the synthetic procedure, the signal is based on Conforming Run Length (CRL). The CRL is the number of samples taken from the process since the previous nonconforming sample until the occurrence of the next nonconforming sample. If the CRL is sufficiently small, then a signal is generated. A comparative study shows that the SyTS chart and the joint X and S charts with double sampling are very similar in performance. However, from the practical viewpoint, the SyTS chart is more convenient to administer than the joint charts.

X charts with supplementary samples to control the mean and variance

A standard X chart for controlling a process takes regular individual observations, for instance every half hour. This article proposes a modification of the X chart that allows one to take supplementary samples. The supplementary sample is taken (and the (X) over bar and R values computed) when the current value of X falls outside the control limits. With the supplementary sample, the signal of out-of-control is given by an (X) over bar value outside the (X) over bar chart's control limits or an R value outside the R chart's control limit. The proposed chart is designed to hold the supplementary sample frequency, during the in-control period, as low as 5% or less. In this context, the practitioner might prefer to verify an out-of-control condition by simply comparing the (X) over bar and R values with the control limits. In other words, without plotting the (X) over bar and R points. The X chart with supplementary samples has two major advantages when compared with the standard (X) over bar and A charts: (a) the user will be plotting X values instead of (X) over bar and R values; (b) the shifts in the process mean and/or changes in the process variance are detected faster.

The causal relationships in mean and variance between stock returns and foreign institutional investment in India

This paper examines the causalities in mean and variance between stock returns and Foreign Institutional Investment (FII) in India. The analysis in this paper applies the Cross Correlation Function approach from Cheung and Ng (1996), and uses daily data for the timeframe of January 1999 to March 2008 divided into two periods before and after May 2003. Empirical results showed that there are uni-directional causalities in mean and variance from stock returns to FII flows irrelevant of the sample periods, while the reverse causalities in mean and variance are only found in the period beginning with 2003. These results point to FII flows having exerted an impact on the movement of Indian stock prices during the more recent period.

Monitoring the mean vector and the covariance ­matrix of multivariate processes with sample means and sample ranges

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Economic design of (X)over-bar and R charts under Weibull shock models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The Aging Process of the Heart: Obesity Is the Main Risk Factor for Left Atrial Enlargement During Aging The MONICA/KORA (Monitoring of Trends and Determinations in Cardiovascular Disease/Cooperative Research in the Region of Augsburg) Study

Objectives This prospective study evaluated the association of obesity and hypertension with left atrial (LA) volume over 10 years. Background Although left atrial enlargement (LAE) is an independent risk factor for atrial fibrillation, stroke, and death, little information is available about determinants of LA size in the general population. Methods Participants (1,212 men and women, age 25 to 74 years) originated from a sex-and age-stratified random sample of German residents of the Augsburg area (MONICA S3). Left atrial volume was determined by standardized echocardiography at baseline and again after 10 years. Left atrial volume was indexed to body height (iLA). Left atrial enlargement was defined as iLA >= 35.7 and >= 33.7 ml/m in men and women, respectively. Results At baseline, the prevalence of LAE was 9.8%. Both obesity and hypertension were independent predictors of LAE, obesity (odds ratio [OR]: 2.4; p < 0.001) being numerically stronger than hypertension (OR: 2.2; p < 0.001). Adjusted mean values for iLA were significantly lower in normal-weight hypertensive patients (25.4 ml/m) than in obese normotensive individuals (27.3 ml/m; p = 0.016). The highest iLA was found in the obese hypertensive subgroup (30.0 ml/m; p < 0.001 vs. all other groups). This group also presented with the highest increase in iLA (+6.0 ml/m) and the highest incidence (31.6%) of LAE upon follow-up. Conclusions In the general population, obesity appears to be the most important risk factor for LAE. Given the increasing prevalence of obesity, early interventions, especially in young obese individuals, are essential to prevent premature onset of cardiac remodeling at the atrial level. (J Am Coll Cardiol 2009; 54: 1982-9) (C) 2009 by the American College of Cardiology Foundation

Electron Beam Welding In-Process Control and Monitoring

This work presents the results of an investigation of processes in the melting zone during Electron Beam Welding(EBW) through analysis of the secondary current in the plasma.The studies show that the spectrum of the secondary emission signal during steel welding has a pronounced periodic component at a frequency of around 15–25 kHz. The signal contains quasi-periodic sharp peaks (impulses). These impulses have stochastically varying amplitude and follow each other inseries, at random intervals between series. The impulses have a considerable current (up to 0.5 A). It was established that during electron-beam welding with the focal spot scanning these impulses follow each other almost periodically. It was shown that the probability of occurrence of these high-frequency perturbation increases with the concentration of energy in the interaction zone. The paper also presents hypotheses for the mechanism of the formation of the high-frequency oscillations in the secondary current signal in the plasma.

Monitoring the domiciliary and peridomiciliary invasion process of Triatoma rubrovaria in the State of Rio Grande do Sul, Brazil

The presence of Triatoma rubrovaria in Brazil has only been confirmed in the States of Paraná and Rio Grande do Sul (RS), where it is found naturally infected with Trypanosoma cruzi. In the wild environment it occurs in rocky habitats and has an eclectic diet, feeding from cockroaches, reptiles and mammals. Data from the Chagas Disease Control Program obtained by the Fundação Nacional de Saúde, between 1975 and 1997, indicate a growing domiciliary and peridomiciliary invasion of T. rubrovaria in RS, where it has become the most frequently Triatominae species captured in this state since the control of Triatoma infestans. In order to monitor this process, we analyzed collection data derived from 22 years of control campaigns against T. infestans. Collection data for triatomines from domestic habitats show an inverse relationship, with high numbers of T. infestans and low numbers of T. rubrovaria during 1976-1987, compared to the following ten years, 1986-1997, when the number of T. infestans dropped drastically and that of T. rubrovaria increased. There are no consistent indications of intradomiciliary colonization by T. rubrovaria, since only low numbers of nymphs have been captured in the intradomiciliary ecotopes. Nevertheless, this species appears to have preadaptive characteristics for anthropic ecotopes, and should be kept under constant epidemiological surveillance.

Economic-statistical design of the (X)over-bar chart used to control a wandering process mean using genetic algorithm

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Control charts for monitoring the mean vector and the covariance matrix of bivariate processes

In this article, we propose new control charts for monitoring the mean vector and the covariance matrix of bivariate processes. The traditional tools used for this purpose are the T (2) and the |S| charts. However, these charts have two drawbacks: (1) the T (2) and the |S| statistics are not easy to compute, and (2) after a signal, they do not distinguish the variable affected by the assignable cause. As an alternative to (1), we propose the MVMAX chart, which only requires the computation of sample means and sample variances. As an alternative to (2), we propose the joint use of two charts based on the non-central chi-square statistic (NCS statistic), named as the NCS charts. Once the NCS charts signal, the user can immediately identify the out-of-control variable. In general, the synthetic MVMAX chart is faster than the NCS charts and the joint T (2) and |S| charts in signaling processes disturbances.

A single chart with supplementary runs rules for monitoring the mean vector and the covariance matrix of multivariate processes

The MRMAX chart is a single chart based on the standardized sample means and sample ranges for monitoring the mean vector and the covariance matrix of multivariate processes. User's familiarity with the computation of these statistics is a point in favor of the MRMAX chart. As a single chart, the recently proposed MRMAX chart is very appropriate for supplementary runs rules. In this article, we compare the supplemented MRMAX chart and the synthetic MRMAX chart with the standard MRMAX chart. The supplementary and the synthetic runs rules enhance the performance of the MRMAX chart. © 2013 Elsevier Ltd.