Monitoring Process Mean and Variability with One Non-central Chi-square Chart

Costa, Antônio Fernando Branco; Rahim, M. A.

doi:10.1080/0266476042000285503

Cited by 69 publications

(36 citation statements)

References 20 publications

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“…Most of the current research has been focused on the Hotelling's T 2 control chart and the multivariate EWMA control chart for controlling the process mean. Yeh et al 16 , Surtihadi et al 17 , Cheng and Thaga 18 and Costa and Rahim 19 propose and study multivariate EWMA and CUSUM control charts to control the dispersion of a multivariate process. As stated before univariate control charts for autocorrelated processes have been discussed in the literature (Montgomery 1 , Box and Luceñno 2 ), however, for multivariate processes the general focus has been placed to uncorrelated processes.…”

Section: Introductionmentioning

confidence: 99%

Multivariate Control Charts Based on Bayesian State Space Models

Triantafyllopoulos

2006

Quality & Reliability Eng

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This paper develops a new multivariate control charting method for vector autocorrelated and serially correlated processes. The main idea is to propose a Bayesian multivariate local level model, which is a generalization of the Shewhart-Deming model for autocorrelated processes, in order to provide the predictive error distribution of the process and then to apply a univariate modified EWMA control chart to the logarithm of the Bayes' factors of the predictive error density versus the target error density. The resulting chart is proposed as capable to deal with both the non-normality and the autocorrelation structure of the log Bayes' factors. The new control charting scheme is general in application and it has the advantage to control simultaneously not only the process mean vector and the dispersion covariance matrix, but also the entire target distribution of the process. Two examples of London metal exchange data and of production time series data illustrate the capabilities of the new control chart.

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Section: Introductionmentioning

confidence: 99%

Multivariate Control Charts Based on Bayesian State Space Models

Triantafyllopoulos

2006

Quality & Reliability Eng

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“…Costa and Rahim 9 showed that this control chart can effectively detect the changes in mean and variance including the decrease in variance. Note that there are three parameters, d 0 , d 1 and L, involved in the testing statistics and there is no exact way to specify them to achieve some nearly 'optimal' performance.…”

Section: Existing Workmentioning

confidence: 98%

A control chart based on likelihood ratio test for monitoring process mean and variability

Zhang

Zou

Wang

2010

Quality & Reliability Eng

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Recently, monitoring the process mean and variance simultaneously by using a single chart has drawn more and more attention. In this paper, we propose a new single chart that integrates the EWMA procedure with the generalized likelihood ratio (GLR) test statistics for jointly monitoring both the process mean and variance. It can be easily designed and constructed, and its average run length can be evaluated by a two-dimensional Markov chain model. Owing to the good properties of the GLR test and EMWA, computation results show that it provides quite a robust and satisfactory performance in various cases, including the detection of the decrease in variability and the individual observation at the sampling point, which are very important in many practical applications but may not be well handled by the existing approaches in the literature. The application of our proposed method is illustrated by a real data example from chemical process control.

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“…Other statistical tools that assists with the quantification and management of variability/heterogeneity not discussed in this paper include chi-square and R charts (Duncan, 1956;Harris and Ross, 1991;Costa and Rahim, 2004;Woodall and Spitzner, 2004). These charts have been extensively used with great success for statistical quality control in the manufacturing and chemical industries.…”

Section: Testing For Heterogeneity In Complex Mining Environmentsmentioning

confidence: 99%

Testing for heterogeneity in complex mining environments

Claassen

2016

J. S. Afr. Inst. Min. Metall.

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Heterogeneity refers to a state or quality of being variable/diverse and comprising different non-compatible elements or parts. In statistical terms a heterogeneous population can refer to a population comprising different non-compatible sub-populations or a multipopulation environment. The latter is commonly found in natural environments such as geological environments (Bardossy and Fodor, 2001). The inherent heterogeneity of complex geological environments is also referred to as spatial heterogeneity. Heterogeneity or variability, however, also occurs over time at mining operations. A case in point is variable ore composition on a conveyance system feeding a processing plant or product stockpile.Heterogeneity associated with the mining environment can significantly influence key aspects of day-to-day mining operations such as sampling, the use of descriptive, probabilistic, and inference calculations, and an operation's ability to manage and control the mining value chain as a whole.The data generated from sampling campaigns forms the basis of nearly all decision-making at the operational, tactical, and strategic levels. As such, it can be argued that the quantity, quality, and correct use of sampling data greatly influence the sustainability of a mining operation.As far as sampling of heterogeneous environments is concerned, an attempt should be made to capture the variability (both spatial and in time) in all key value chain performance drivers through representative or random sampling. According to the theory of sampling developed by Pierre Gy (1983), sampling errors are induced mainly by high levels of heterogeneity of the population being sampled.Descriptive statistics are used on a daily basis in mining operations to calculate values such as the average, median, range, and standard deviation of a known data-set. Probabilistic and inference statistics are less frequently employed. Probabilistic statistics (based on probability theory) are used to determine the likelihood or degree of certainty/uncertainty of outcomes drawn from a known population, i.e. if the population is known, what can be deduced from the samples taken from it?Inference statistics are used to describe an unknown population if everything about the sample is known (random sampling required). Inference statistics involve tests of hypotheses, confidence intervals, and regression.Testing for heterogeneity in complex mining environments by J.O. Claassen* Homogeneous populations are required to perform descriptive, probabilistic, and inference statistics and to support stable, predictable mining operations. The geological and downstream processing environments are, however, highly heterogeneous. The complex nature of mining environments requires means to identify and define multipopulation environments that could affect the performance of mining value chains. A study performed at several operating mines suggests that the impact of heterogeneous or variable geological, mining, and plant processing environments on overall mining value chain per...

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Monitoring Process Mean and Variability with One Non-central Chi-square Chart

Cited by 69 publications

References 20 publications

Multivariate Control Charts Based on Bayesian State Space Models

Multivariate Control Charts Based on Bayesian State Space Models

A control chart based on likelihood ratio test for monitoring process mean and variability

Testing for heterogeneity in complex mining environments

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