Double sampling (x)over-bar control chart for a first-order autoregressive moving average process model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Variable parameter and double sampling (X)over-bar charts in the presence of correlation: The Markov chain approach

The general assumption under which the (X) over bar chart is designed is that the process mean has a constant in-control value. However, there are situations in which the process mean wanders. When it wanders according to a first-order autoregressive (AR (1)) model, a complex approach involving Markov chains and integral equation methods is used to evaluate the properties of the (X) over bar chart. In this paper, we propose the use of a pure Markov chain approach to study the performance of the (X) over bar chart. The performance of the chat (X) over bar with variable parameters and the (X) over bar with double sampling are compared. (C) 2011 Elsevier B.V. All rights reserved.

Bivariate control charts with double sampling

In this article, we consider the T(2) chart with double sampling to control bivariate processes (BDS chart). During the first stage of the sampling, n(1) items of the sample are inspected and two quality characteristics (x; y) are measured. If the Hotelling statistic T(1)(2) for the mean vector of (x; y) is less than w, the sampling is interrupted. If the Hotelling statistic T(1)(2) is greater than CL(1), where CL(1) > w, the control chart signals an out-of-control condition. If w < T(1)(2) <= CL(1), the sampling goes on to the second stage, where the remaining n(2) items of the sample are inspected and T(2)(2) for the mean vector of the whole sample is computed. During the second stage of the sampling, the control chart signals an out-of-control condition when the statistic T(2)(2) is larger than CL(2). A comparative study shows that the BDS chart detects process disturbances faster than the standard bivariate T(2) chart and the adaptive bivariate T(2) charts with variable sample size and/or variable sampling interval.

The double sampling and the EWMA charts based on the sample variances

We propose a new statistic to control the covariance matrix of bivariate processes. This new statistic is based on the sample variances of the two quality characteristics, in short VMAX statistic. The points plotted on the chart correspond to the maximum of the values of these two variances. The reasons to consider the VMAX statistic instead of the generalized variance vertical bar S vertical bar is its faster detection of process changes and its better diagnostic feature; that is, with the VMAX statistic it is easier to identify the out-of-control variable. We study the double sampling (DS) and the exponentially weighted moving average (EWMA) charts based on the VMAX statistic. (C) 2008 Elsevier B.V. All rights reserved.

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.

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.

Gráfico de controle de VMAX para o monitoramento da matriz de covariâncias

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

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 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.

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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

X̄ 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 X̄ 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) X̄ chart are obtained using Markov chains. The VSS X̄ chart is substantially quicker than the traditional X̄ chart in detecting moderate shifts in the process.

Estudo das propriedades dos gráficos de controle bivariados com amostragem dupla

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Gráficos de controle de X para monitoramento de processos autocorrelacionados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Gráficos de controle para monitoramento de processos multivariados

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

Estimating cyclopoid copepod species richness and geographical distribution (Crustacea) across a large hydrographical basin: comparing between samples from water column (plankton) and macrophyte stands

Species richness and geographical distribution of Cyclopoida freshwater copepods were analyzed along the La Plata River basin. Ninety-six samples were taken from 24 sampling sites, twelve sites for zooplankton in open waters and twelve sites for zooplankton within macrophyte stands, including reservoirs and lotic stretches. There were, on average, three species per sample in the plankton compared to five per sample in macrophytes. Six species were exclusive to the plankton, 10 to macrophyte stands, and 17 were common to both. Only one species was found in similar proportions in plankton and macrophytes, while five species were widely found in plankton, and thirteen in macrophytes. The distinction between species from open water zooplankton and macrophytes was supported by nonmetric multidimensional analysis. There was no distinct pattern of endemicity within the basin, and double sampling contributes to this result. This lack of sub-regional faunal differentiation is in accordance with other studies that have shown that cyclopoids generally have wide geographical distribution in the Neotropics and that some species there are cosmopolitan. This contrasts with other freshwater copepods such as Calanoida and some Harpacticoida. We conclude that sampling plankton and macrophytes together provided a more accurate estimate of the richness and geographical distribution of these organisms than sampling in either one of those zones alone.