VSSI (X)over-bar charts with sampling at fixed times

A standard (X) over bar chart for controlling the process mean takes samples of size no at specified, equally-spaced, fixed-time points. This article proposes a modification of the standard (X) over bar chart that allows one to take additional samples, bigger than no, between these fixed times. The additional samples are taken from the process when there is evidence that the process mean moved from target. Following the notation proposed by Reynolds (1996a) and Costs (1997) we shortly call the proposed (X) over bar chart as VSSIFT (X) over bar chart: where VSSIFT means variable sample size and sampling intervals with fixed times. The (X) over bar chart with the VSSIFT feature is easier to be administered than a standard VSSI (X) over bar chart that is not constrained to sample at the specified fixed times. The performances of the charts in detecting process mean shifts are comparable.

Economic design of (X)over-bar charts with variable parameters: the Markov chain approach

This paper presents an economic design of (X) over bar control charts with variable sample sizes, variable sampling intervals, and variable control limits. The sample size n, the sampling interval h, and the control limit coefficient k vary between minimum and maximum values, tightening or relaxing the control. The control is relaxed when an (X) over bar value falls close to the target and is tightened when an (X) over bar value falls far from the target. A cost model is constructed that involves the cost of false alarms, the cost of finding and eliminating the assignable cause, the cost associated with production in an out-of-control state, and the cost of sampling and testing. 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 comprehensive study is performed to examine the economic advantages of varying the (X) over bar chart parameters.

A stochastic shift model for economically designed charts constrained by the process stage configuration

An economic model including the labor resource and the process stage configuration is proposed to design g charts allowing for all the design parameters to be varied in an adaptive way. A random shift size is considered during the economic design selection. The results obtained for a benchmark of 64 process stage scenarios show that the activities configuration and some process operating parameters influence the selection of the best control chart strategy: to model the random shift size, its exact distribution can be approximately fitted by a discrete distribution obtained from a relatively small sample of historical data. However, an accurate estimation of the inspection costs associated to the SPC activities is far from being achieved. An illustrative example shows the implementation of the proposed economic model in a real industrial case. (C) 2011 Elsevier B.V. All rights reserved.

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.

VSSI X̄ charts with sampling at fixed times

A standard X̄ chart for controlling the process mean takes samples of size n0 at specified, equally-spaced, fixed-time points. This article proposes a modification of the standard X chart that allows one to take additional samples, bigger than n0, between these fixed times. The additional samples are taken from the process when there is evidence that the process mean moved from target. Following the notation proposed by Reynolds (1996a) and Costa (1997) we shortly call the proposed X chart as VSSIFT X chart where VSSIFT means variable sample size and sampling intervals with fixed times. The X chart with the VSSIFT feature is easier to be administered than a standard VSSI X chart that is not constrained to sample at the specified fixed times. The performances of the charts in detecting process mean shifts are comparable. Copyright © 1998 by Marcel Dekker, Inc.

X̄ Charts with Variable Parameters

Varying the parameters of the X̄ chart has been explored extensively in recent years. In this paper, we extend the study of the X̄ chart with variable parameters to include variable action limits. The action limits establish whether the control should be relaxed or not. When the X̄ 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 X̄ 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 X̄ chart more powerful than the CUSUM scheme in detecting shifts in the process mean.

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.

Preliminary results concerning the VSS X- chart with unknow in-control parameters

The VSS X- chart is known to perform better than the traditional X- control chart in detecting small to moderate mean shifts in the process. Many researchers have used this chart in order to detect a process mean shift under the assumption of known parameters. However, in practice, the process parameters are rarely known and are usually estimated from an in-control Phase I data set. In this paper, we evaluate the (run length) performances of the VSS X- control chart when the process parameters are estimated and we compare them in the case where the process parameters are assumed known. We draw the conclusion that these performances are quite different when the shift and the number of samples used during the phase I are small. ©2010 IEEE.

Attribute charts for monitoring the mean vector of bivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Joint X̄ and R charts with variable parameters

Recent studies have shown that the X̄chart with variable parameters (Vp X̄ chart) detects process shifts faster than the traditional X̄ chart. This article extends these studies for processes that are monitored by both, X̄ and R charts. Basically, the X̄ and R values establish if the control should or should not be relaxed. When the X̄ and R values fall in the central region the control is relaxed because one will wait more to take the next sample and/or the next sample will be smaller than usual. When the X̄ or R values fall in the warning region the control is tightened because one will wait less to take the next sample and the next sample will be larger than usual. The action limits are also made variable. This paper proposes to draw the action limits (for both charts) wider than usual, when the control is relaxed and narrower than usual when the control is tightened. The Vp feature improves the joint X̄ and R control chart performance in terms of the speed with which the process mean and/or variance shifts are detected. © 1998 IIE.

Perdas de grãos e distribuição de palha na colheita mecanizada de soja

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

A new chart based on sample variances for monitoring the covariance matrix of multivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A new chart for monitoring the covariance matrix of bivariate processes

In this article we consider a control chart based on the sample variances of two quality characteristics. The points plotted on the chart correspond to the maximum value of these two statistics. The main reason to consider the proposed chart instead of the generalized variance |S| chart is its better diagnostic feature, that is, with the new chart it is easier to relate an out-of-control signal to the variables whose parameters have moved away from their in-control values. We study the control chart efficiency considering different shifts in the covariance matrix. In this way, we obtain the average run length (ARL) that measures the effectiveness of a control chart in detecting process shifts. The proposed chart always detects process disturbances faster than the generalized variance |S| chart. The same is observed when the size of the samples is variable, except in a few cases in which the size of the samples switches between small size and very large size.

Caracterização das perdas e distribuição de cobertura vegetal em colheita mecanizada de soja

O conceito de controle de qualidade nas operações inserido na agricultura é viabilizado por incidir diretamente nos principais objetivos do processo produtivo: retorno econômico e aumento da produtividade. A colheita mecanizada normalmente é realizada sem que haja controle efetivo para que a variabilidade das perdas fique dentro de padrões aceitáveis. Esta pesquisa teve o objetivo de determinar e caracterizar as perdas e a distribuição da cobertura vegetal após a colheita mecanizada da soja, por meio de ferramenta de controle estatístico de processo (cartas de controle). A média da perda de grãos total foi próxima do limite superior aceitável para a cultura da soja, apresentando alta variabilidade entre os pontos, tornando o processo fora de controle. A distribuição de cobertura vegetal manteve-se em processo controlado, com maior variabilidade onde o relevo foi mais inclinado. A utilização das cartas de controle foi eficiente na identificação dos pontos fora de controle e na avaliação da qualidade do processo de colheita.