Th e Non-Central Chi-Square Chart with Double Sampling

In this article, we consider a non-central chi-square chart with double sampling (DS χ2 chart) to control the process mean and variance. As in the case of Shewhart control charts, samples of fi xed size are taken from the process at regular time intervals; however, the sampling is performed in two stages. Let X be the process quality variable being measured. During the fi rst stage, one item of the sample is inspected; if its X value 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 a non-central chi-square statistic, say T, is computed taking into account all n items of the sample, that is, their X values. A signal is triggered when the sample point given by the T value falls above the upper control limit of the proposed chart. The DS χ2 chart performs better than the joint X and R charts, except when there is a large change in the process mean. Furthermore, if the DS χ2 chart is used for monitoring diameters, volumes, weights, etc., then the employment of appropriate devices, such as go-no-go gauges can reduce the effort to decide if the sampling should go to the second stage or not

Optimal linear combination of poisson variables for multivariate statistical process control

In this paper we analyze the monitoring of p Poisson quality characteristics simultaneously, developing a new multivariate control chart based on the linear combination of the Poisson variables, the LCP control chart. The optimization of the coefficients of this linear combination (and control limit) for minimizing the out-of-control ARL is constrained by the desired in-control ARL. In order to facilitate the use of this new control chart the optimization is carried out employing user-friendly Windows© software, which also makes a comparison of performance between this chart and other schemes based on monitoring a set of Poisson variables; namely a control chart on the sum of the variables (MP chart), a control chart on their maximum (MX chart) and an optimized set of univariate Poisson charts (Multiple scheme). The LCP control chart shows very good performance. First, the desired in-control ARL (ARL0) is perfectly matched because the linear combination of Poisson variables is not constrained to integer values, which is an advantage over the rest of charts, which cannot in general match the required ARL0 value. Second, in the vast majority of cases this scheme signals process shifts faster than the rest of the charts.This work has been supported by the Ministry of Education and Science of Spain, research project number DPI2009-09925, the CNPq (the Brazilian Council for Scientific and Technological Development), project numbers 302326/2008-1 and 473706/2010-5, and SENESCYT-Ecuador (National Secretary of Higher Education, Science, Technology and Innovation of Equator). The authors are grateful to the referees for their comments, which led to significant improvement of the paper.Kahn Epprecht, E.; Aparisi García, FJ.; García Bustos, SL. (2013). Optimal linear combination of poisson variables for multivariate statistical process control. Computers and Operations Research. 40(12):3021-3032. https://doi.org/10.1016/j.cor.2013.07.007S30213032401

Economic design of a Vp X̄ chart

We develop an economic model for X̄ control charts having all design parameters varying in an adaptive way, that is, in real time considering current sample information. In the proposed model, each of the design parameters can assume two values as a function of the most recent process information. The cost function is derived and it provides a device for optimal selection of the design parameters. Through a numerical example one can foresee the savings that the developed model possibly provides. © 2001 Elsevier Science B.V. All rights reserved

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

In this paper, we propose a synthetic control chart with two-stage testing (SyTS chart) to control the process mean and variance. As in the case of Shewhart control charts, samples are taken from the process at regular time intervals; however, testing is performed in two stages. During the first stage, one item of the sample is inspected; if its value is close to the target value of the process mean, then this terminates testing. Otherwise, the testing goes on to the second stage, where the remaining items are inspected and a non-central chi-square statistic is computed taking into account all items of the sample. When this statistic is larger than a specified value, the sample is classified as nonconforming. According to the synthetic procedure, the signal is based on the conforming run length (CRL). A comparative study shows that the SyTS chart and the joint (X) over bar and S charts with double sampling are very similar in performance. However, from a practical viewpoint, it is more convenient to monitor the process by looking at only one chart rather than looking at two charts separately. Comparisons with the joint (X) over bar and S charts and with several CUSUM schemes show that the SyTS chart has better overall performance.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Performance Comparisons of EWMA Control Chart Schemes

Combining an EWMA chart with a Shewhart chart is traditionally recommended as a means of providing good protection against both small and large shifts in the process mean. Capizzi and Masarotto have proposed an EWMA chart with a variable smoothing constant (AEWMA) for the same purpose. In this paper, we optimize the designs of the AEWMA and of the combined EWMA-Shewhart schemes with regard to pairs of shifts in the process mean and compare their performances. When the schemes are optimized for the same pair of shifts, their ARL profiles practically coincide. The choice between the AEWMA and the EWMA-Shewhart scheme then becomes a matter of personal preference. We also explore using an AEWMA together with a Shewhart chart, but we find no performance improvement. An additional contribution of this paper is the tables of optimal designs of each scheme for several pairs of shifts.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

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

Um modelo de minimização de custos em diagnósticos com um caso de aplicação em um banco de sangue

O problema aqui tratado é, dado um conjunto de testes para determinação de um diagnóstico, determinar a seqüência de execução destes testes com custo esperado mínimo. Assumindo algumas hipóteses simplificadoras, apresenta-se uma solução que fornece diretamente a seqüência ótima, eliminando a necessidade de busca. A solução se estende também a uma versão do problema com uma estrutura hierárquica de testes. O modelo é genérico, podendo aplicar-se a diagnósticos nos mais diversos contextos: de problemas de processos em controle de qualidade, de falhas de equipamentos, ou no contexto médico. É apresentada uma extensão do modelo, para situações em que algumas das hipóteses básicas do modelo original não se aplicam. Esta extensão foi motivada por um problema real, de minimização de gastos com exames sorológicos em um banco de sangue. A solução obtida para esse problema resultou em economia substancial.<br>This work deals with the following problem: given a set of tests for a diagnosis problem, find the minimum-cost order of execution of the tests. It is shown that under some simplifying assumptions, graph search is obviated by a very straightforward solution. This solution is also applicable to situations in which the tests follow a hierarchical organization. The model is generic, with no restriction of context: it is applicable to the diagnosis of equipment failures, of problems with processes in the context of quality control, or to medical diagnosis. An extension of the basic model for the situation in which some of the simplifying assumptions are not applicable is presented. This extension was motivated by a real problem, and the solution obtained led to significant cost reduction