Joint (X)over-bar and R charts with variable sample sizes and sampling intervals

Recent studies have shown that the (X) over bar chart with variable sampling intervals (VSI) and/or with variable sample sizes (VSS) detects process shifts faster than the traditional (X) over bar chart. This article extends these studies for processes that are monitored by both the (X) over bar and R charts. A Markov chain model is used to determine the properties of the joint (X) over bar and R charts with variable sample sizes and sampling intervals (VSSI). The VSSI scheme improves the joint (X) over bar and R control chart performance in terms of the speed with which shifts in the process mean and/or variance are detected.

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)over-bar charts with variable parameters

Varying the parameters of the (X) over bar chart has been explored extensively in recent years. In this paper, we extend the study of the (X) over bar chart with variable parameters to include variable action limits. The action limits establish whether the control should be relaxed or not. When the (X) over bar falls near the target, the control is relaxed so that there will be more time before the next sample and/or the next sample will be smaller than usual. When the (X) over bar falls far from the target but not in the action region, the control is tightened so that there is less time before the next sample and/or the next sample will be larger than usual. The goal is to draw the action limits wider than usual when the control is relaxed and narrower than usual when the control is tightened. This new feature then makes the (X) over bar chart more powerful than the CUSUM scheme in detecting shifts in the process mean.

Joint (X)over-bar and R charts with two-stage samplings

When joint (X) over bar and R charts are in use, samples of fixed size are regularly taken from the process, and their means and ranges are plotted on the (X) over bar and R charts, respectively. In this article, joint (X) over bar and R charts have been used for monitoring continuous production processes. The sampling is performed, in two stages. During the first stage, one item of the sample is inspected and, depending on the result, the sampling is interrupted if the process is found to be in control; otherwise, it goes on to the second stage, where the remaining sample items are inspected. The two-stage sampling procedure speeds up the detection of process disturbances. The proposed joint (X) over bar and R charts are easier to administer and are more efficient than the joint (X) over bar and R charts with variable sample size where the quality characteristic of interest can be evaluated either by attribute or variable. Copyright (C) 2004 John Wiley Sons, Ltd.

Economic design of two-stage (X)over-bar charts: the Markov chain approach

When the (X) over bar chart is in use, samples are regularly taken from the process, and their means are plotted on the chart. In some cases, it is too expensive to obtain the X values, but not the values of a correlated variable Y. This paper presents a model for the economic design of a two-stage control chart, that is. a control chart based on both performance (X) and surrogate (Y) variables. The process is monitored by the surrogate variable until it signals an out-of-control behavior, and then a switch is made to the (X) over bar chart. The (X) over bar chart is built with central, warning. and action regions. If an X sample mean falls in the central region, the process surveillance returns to the (Y) over bar chart. Otherwise. The process remains under the (X) over bar chart's surveillance until an (X) over bar sample mean falls outside the control limits. The search for an assignable cause is undertaken when the performance variable signals an out-of-control behavior. In this way, the two variables, are used in an alternating fashion. The assumption of an exponential distribution to describe the length of time the process remains in control allows the application of the Markov chain approach for developing the cost function. A study is performed to examine the economic advantages of using performance and surrogate variables. (C) 2003 Elsevier B.V. All rights reserved.

(X)OVER-BAR CHARTS WITH VARIABLE SAMPLE-SIZE

The usual practice in using a control chart to monitor a process is to take samples of size n from the process every h hours This article considers the properties of the XBAR chart when the size of each sample depends on what is observed in the preceding sample. The idea is that the sample should be large if the sample point of the preceding sample is close to but not actually outside the control limits and small if the sample point is close to the target. The properties of the variable sample size (VSS) XBAR chart are obtained using Markov chains. The VSS XBAR chart is substantially quicker than the traditional XBAR chart in detecting moderate shifts in the process.

Bayesian and multivariate methods applied to favorability quantification in recôncavo Basin and Ribeira Belt, Brazil

A methodology to define favorable areas in petroleum and mineral exploration is applied, which consists in weighting the exploratory variables, in order to characterize their importance as exploration guides. The exploration data are spatially integrated in the selected area to establish the association between variables and deposits, and the relationships among distribution, topology, and indicator pattern of all variables. Two methods of statistical analysis were compared. The first one is the Weights of Evidence Modeling, a conditional probability approach (Agterberg, 1989a), and the second one is the Principal Components Analysis (Pan, 1993). In the conditional method, the favorability estimation is based on the probability of deposit and variable joint occurrence, with the weights being defined as natural logarithms of likelihood ratios. In the multivariate analysis, the cells which contain deposits are selected as control cells and the weights are determined by eigendecomposition, being represented by the coefficients of the eigenvector related to the system's largest eigenvalue. The two techniques of weighting and complementary procedures were tested on two case studies: 1. Recôncavo Basin, Northeast Brazil (for Petroleum) and 2. Itaiacoca Formation of Ribeira Belt, Southeast Brazil (for Pb-Zn Mississippi Valley Type deposits). The applied methodology proved to be easy to use and of great assistance to predict the favorability in large areas, particularly in the initial phase of exploration programs. © 1998 International Association for Mathematical Geology.

Joint X̄ and R Charts with Variable Sample Sizes and Sampling Intervals

Recent studies have shown that the X̄ chart with variable sampling intervals (VSI) and/or with variable sample sizes (VSS) detects process shifts faster than the traditional X̄ chart. This article extends these studies for processes that are monitored by both the X̄ and R charts. A Markov chain model is used to determine the properties of the joint X and R charts with variable sample sizes and sampling intervals (VSSI). The VSSI scheme improves the joint X̄ and R control chart performance in terms of the speed with which shifts in the process mean and/or variance are detected.

Psychiatric disorders and psychiatric consultation in a general hospital: A case- control study

Introduction: Psychiatric consultation (PC) has been considered an efficient tool to develop research, to track and to give assistance benefiting patients, health professionals and the institution. However, it has not been much used in Brazil. Although 30 to 50% of general hospital (GH) inpatients may present a psychiatric disorder, only 1 to 12% of them are referred to assessment. The aims of this study were: to assess mental disorders in a GH; to identify which of these patients are sent to psychiatric care; to verify alleged reasons for referral to psychiatric consultation, and to examine the relationship between PC and psychiatric learning (during medical school and residence). Methods: A case-control patient study was conducted (47 cases and 94 controls) to analyze in detail the following variables: socio-demographic; clinical; degree of information (about the disease and diagnostic/therapeutic procedures), and relationship between patient and health team. Psychiatric diagnoses were made according to the ICD- 10 criteria. The Self Report Questionnaire (SRQ), the CAGE and Brief Psychiatric Rating Scale (BPRS) were used as well as a specifically designed questionnaire to collect clinical and demographic data. Results: Behavioral alterations, either of elation or of depression, were the main for requesting a PC; 95.8% of the cases and 27.7% of the controls had a mental disorder. Organic mental disorders and alcohol-related disorders were the most frequent diagnoses in group I (cases), while anxiety, depressive and alcohol-related disorders were predominant in group II (controls). Control group patients were better informed and more able to establish an appropriate relationship with the health team than case patients. The logistic regression showed CAGE-positive patients having 12.85 times greater risk of being referred to PC, followed by unemployed patients (2.44 times more PC referrals). Discussion: The SRQ and CAGE were quite useful in the screening of possible patients and might be important for medical students to learn and use as generalists. Further research is needed to verify if and how the newly-established service will improve the diagnostic and treatment skills of our students.

Evaluation of the combined solar TiO2/photo-Fenton process using multivariate analysis

The effect of combining the photocatalytic processes using TiO 2 and the photo-Fenton reaction with Fe3+ or ferrioxalate as a source of Fe2+ was investigated in the degradation of 4-chlorophenol (4CP) and dichloroacetic acid (DCA) using solar irradiation. Multivariate analysis was used to evaluate the role of three variables: iron, H2O2 and TiO2 concentrations. The results show that TiO2 plays a minor role when compared to iron and H2O2 in the solar degradation of 4CP and DCA in the studied conditions. However, its presence can improve TOC removal when H2O2 is totally consumed. Iron and peroxide play major roles, especially when Fe(NO3)3 used in the degradation of 4CP. No significant synergistic effect was observed by the addition of TiO 2 in this process. On the other hand, synergistic effects were observed between FeOx and TiO2 and between H 2O2 and TiO2 in the degradation of DCA. © IWA Publishing 2004.

Double sampling X̄ control chart for a first order autoregressive process

In this paper we propose the Double Sampling X̄ control chart for monitoring processes in which the observations follow a first order autoregressive model. We consider sampling intervals that are sufficiently long to meet the rational subgroup concept. The Double Sampling X̄ chart is substantially more efficient than the Shewhart chart and the Variable Sample Size chart. To study the properties of these charts we derived closed-form expressions for the average run length (ARL) taking into account the within-subgroup correlation. Numerical results show that this correlation has a significant impact on the chart properties.

A Multivariate Calibration Procedure for UV/VIS Spectrometric Monitoring of BHK-21 Cell Metabolism and Growth

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

The steady-state behavior of the synthetic and side-sensitive synthetic double sampling (X)over-bar charts

The steady-state average run length is used to measure the performance of the recently proposed synthetic double sampling (X) over bar chart (synthetic DS chart). The overall performance of the DS X chart in signaling process mean shifts of different magnitudes does not improve when it is integrated with the conforming run length chart, except when the integrated charts are designed to offer very high protection against false alarms, and the use of large samples is prohibitive. The synthetic chart signals when a second point falls beyond the control limits, no matter whether one of them falls above the centerline and the other falls below it; with the side-sensitive feature, the synthetic chart does not signal when they fall on opposite sides of the centerline. We also investigated the steady-state average run length of the side-sensitive synthetic DS X chart. With the side-sensitive feature, the overall performance of the synthetic DS X chart improves, but not enough to outperform the non-synthetic DS X chart. Copyright (C) 2014 John Wiley &Sons, Ltd.