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.

Quality Control in the Healthcare Industry: An Analysis of Surgery Turnover Times

For virtually all hospitals, utilization rates are a critical managerial indicator of efficiency and are determined in part by turnover time. Turnover time is defined as the time elapsed between surgeries, during which the operating room is cleaned and preparedfor the next surgery. Lengthier turnover times result in lower utilization rates, thereby hindering hospitals’ ability to maximize the numbers of patients that can be attended to. In this thesis, we analyze operating room data from a two year period provided byEvangelical Community Hospital in Lewisburg, Pennsylvania, to understand the variability of the turnover process. From the recorded data provided, we derive our best estimation of turnover time. Recognizing the importance of being able to properly modelturnover times in order to improve the accuracy of scheduling, we seek to fit distributions to the set of turnover times. We find that log-normal and log-logistic distributions are well-suited to turnover times, although further research must validate this finding. Wepropose that the choice of distribution depends on the hospital and, as a result, a hospital must choose whether to use the log-normal or the log-logistic distribution. Next, we use statistical tests to identify variables that may potentially influence turnover time. We find that there does not appear to be a correlation between surgerytime and turnover time across doctors. However, there are statistically significant differences between the mean turnover times across doctors. The final component of our research entails analyzing and explaining the benefits of introducing control charts as a quality control mechanism for monitoring turnover times in hospitals. Although widely instituted in other industries, control charts are notwidely adopted in healthcare environments, despite their potential benefits. A major component of our work is the development of control charts to monitor the stability of turnover times. These charts can be easily instituted in hospitals to reduce the variabilityof turnover times. Overall, our analysis uses operations research techniques to analyze turnover times and identify manners for improvement in lowering the mean turnover time and thevariability in turnover times. We provide valuable insight into a component of the surgery process that has received little attention, but can significantly affect utilization rates in hospitals. Most critically, an ability to more accurately predict turnover timesand a better understanding of the sources of variability can result in improved scheduling and heightened hospital staff and patient satisfaction. We hope that our findings can apply to many other hospital settings.

Control estadístico de calidad en bibliotecología : Aplicación de gráficos de control en los procesos técnicos

A partir de la aceptación de la biblioteca como parte del ciclo de creación, organización y diseminación del conocimiento cambió el concepto de la misma de una entidad cerrada hacia un sistema dinámico en constante interacción con su entorno. Así se la reconoció como una institución social más que como una colección de documentos. Desde entonces se percibió a la biblioteca como una entidad en la que se podía aplicar los principios de gestión. Desde entonces se utilizaron distintas herramientas de gestión para la toma de decisiones en el ámbito de las bibliotecas. Entre estas herramientas son de gran importancia en el control estadístico de procesos los gráficos de control, utilizados para medir la estabilidad de un proceso a través del tiempo. Han tenido amplia aplicación en el control estadístico de la calidad, comenzando en el ámbito industrial. Hoy su aplicación se ha extendido a una gran variedad de disciplinas incluyen empresas de servicios y unidades administrativas. Aquí se presentan a los gráficos de control como una importante herramienta de gestión aplicada a los procesos técnicos permitiendo su evaluación y el monitoreo de su desempeño a partir de la utilización de indicadores y otros datos de carácter diagnóstico

Control estadístico de calidad en bibliotecología : Aplicación de gráficos de control en los procesos técnicos

A partir de la aceptación de la biblioteca como parte del ciclo de creación, organización y diseminación del conocimiento cambió el concepto de la misma de una entidad cerrada hacia un sistema dinámico en constante interacción con su entorno. Así se la reconoció como una institución social más que como una colección de documentos. Desde entonces se percibió a la biblioteca como una entidad en la que se podía aplicar los principios de gestión. Desde entonces se utilizaron distintas herramientas de gestión para la toma de decisiones en el ámbito de las bibliotecas. Entre estas herramientas son de gran importancia en el control estadístico de procesos los gráficos de control, utilizados para medir la estabilidad de un proceso a través del tiempo. Han tenido amplia aplicación en el control estadístico de la calidad, comenzando en el ámbito industrial. Hoy su aplicación se ha extendido a una gran variedad de disciplinas incluyen empresas de servicios y unidades administrativas. Aquí se presentan a los gráficos de control como una importante herramienta de gestión aplicada a los procesos técnicos permitiendo su evaluación y el monitoreo de su desempeño a partir de la utilización de indicadores y otros datos de carácter diagnóstico

Control estadístico de calidad en bibliotecología : Aplicación de gráficos de control en los procesos técnicos

A partir de la aceptación de la biblioteca como parte del ciclo de creación, organización y diseminación del conocimiento cambió el concepto de la misma de una entidad cerrada hacia un sistema dinámico en constante interacción con su entorno. Así se la reconoció como una institución social más que como una colección de documentos. Desde entonces se percibió a la biblioteca como una entidad en la que se podía aplicar los principios de gestión. Desde entonces se utilizaron distintas herramientas de gestión para la toma de decisiones en el ámbito de las bibliotecas. Entre estas herramientas son de gran importancia en el control estadístico de procesos los gráficos de control, utilizados para medir la estabilidad de un proceso a través del tiempo. Han tenido amplia aplicación en el control estadístico de la calidad, comenzando en el ámbito industrial. Hoy su aplicación se ha extendido a una gran variedad de disciplinas incluyen empresas de servicios y unidades administrativas. Aquí se presentan a los gráficos de control como una importante herramienta de gestión aplicada a los procesos técnicos permitiendo su evaluación y el monitoreo de su desempeño a partir de la utilización de indicadores y otros datos de carácter diagnóstico

ARL1 of the Attribute c Control Chart with Estimated Parameter

International audience

Critical applications of SW 846 US EPA methods to evaluation of marine samples quality

Technical evaluation of analytical data is of extreme relevance considering it can be used for comparisons with environmental quality standards and decision-making as related to the management of disposal of dredged sediments and the evaluation of salt and brackish water quality in accordance with CONAMA 357/05 Resolution. It is, therefore, essential that the project manager discusses the environmental agency's technical requirements with the laboratory contracted for the follow-up of the analysis underway and even with a view to possible re-analysis when anomalous data are identified. The main technical requirements are: (1) method quantitation limits (QLs) should fall below environmental standards; (2) analyses should be carried out in laboratories whose analytical scope is accredited by the National Institute of Metrology (INMETRO) or qualified or accepted by a licensing agency; (3) chain of custody should be provided in order to ensure sample traceability; (4) control charts should be provided to prove method performance; (5) certified reference material analysis or, if that is not available, matrix spike analysis, should be undertaken and (6) chromatograms should be included in the analytical report. Within this context and with a view to helping environmental managers in analytical report evaluation, this work has as objectives the discussion of the limitations of the application of SW 846 US EPA methods to marine samples, the consequences of having data based on method detection limits (MDL) and not sample quantitation limits (SQL), and present possible modifications of the principal method applied by laboratories in order to comply with environmental quality standards.

Economic design of an X chart for short-run production

The aim of this paper is to present an economical design of an X chart for a short-run production. The process mean starts equal to mu(0) (in-control, State I) and in a random time it shifts to mu(1) > mu(0) (out-of-control, State II). The monitoring procedure consists of inspecting a single item at every m produced ones. If the measurement of the quality characteristic does not meet the control limits, the process is stopped, adjusted, and additional (r - 1) items are inspected retrospectively. The probabilistic model was developed considering only shifts in the process mean. A direct search technique is applied to find the optimum parameters which minimizes the expected cost function. Numerical examples illustrate the proposed procedure. (C) 2009 Elsevier B.V. All rights reserved.

Controle estatístico de processo aplicado no monitoramento da absorção de água por carcaças de frango durante a etapa de pré-resfriamento

A absorção de água por carcaças de frango na etapa de pré-resfriamento da linha abate representa uma característica de qualidade importante relacionada ao rendimento do produto final. Uma forma de manter o padrão de qualidade de um produto é garantir que as etapas do processo sejam estáveis e replicáveis. Ao empregar o Controle Estatístico de Processo (CEP) é possível obter estabilidade e melhorias nos processos, por meio da redução da variabilidade. Neste contexto, o objetivo deste trabalho foi a aplicação de gráficos de controle, análise de correlação, estatística descritiva, testes de hipóteses e regressão linear múltipla na linha de abate de um abatedouro-frigorífico de aves para monitorar a variabilidade da absorção de água pelas carcaças de frango após a etapa de pré-resfriamento. Como resultado, verificou-se que o teor de absorção de água das carcaças de frango apresentou elevada variabilidade, sendo que 10% (8/80) das carcaças apresentaram absorção de água superior ao limite de 8% definido pela legislação brasileira. Do total de 16 variáveis de entrada analisadas, as mais impactantes no teor de absorção de água foram o “tempo de retenção da carcaça no pré-chiller” e o “tempo de espera da carcaça após a etapa de gotejamento”. Entretanto, o modelo de regressão obtido apresentou baixa correlação (R²=0,16) que foi associada à elevada variabilidade da variável-resposta. Os resultados da estatística descritiva demonstraram que as variáveis de entrada também apresentaram elevada variabilidade, com coeficiente de variação entre 7,95 e 63,5%. Verificou-se, pela análise dos gráficos de controle de medida individual e da amplitude móvel, que 15 das 16 variáveis de entrada se apresentaram fora de controle estatístico assim como a variável-resposta. Baseado no fluxograma e na descrição das etapas da linha de abate, previamente realizados, atribuiu-se à falta de padronização na condução das etapas e de procedimentos para o controle de qualidade das operações na linha de abate como fatores relevantes que poderiam estar associados à presença de causas especiais no processo. Concluiu-se que para reduzir a elevada variabilidade das variáveis e eliminar as causas especiais presentes são necessários ajustes operacionais para, dessa forma, obter um processo mais estável e mais uniforme garantindo o padrão de qualidade das carcaças de frango em relação ao teor de absorção de água.