20,486 research outputs found
Multivariate control charts based on Bayesian state space models
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.Comment: 19 pages, 6 figure
Multivariate Statistical Process Control Charts: An Overview
In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.quality control, process control, multivariate statistical process control, Hotelling's T-square, CUSUM, EWMA, PCA, PLS
Contributions to improve the power, efficiency and scope of control-chart methods : a thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Statistics at Massey University, Albany, New Zealand
Listed in 2019 Dean's List of Exceptional ThesesDetection of outliers and other anomalies in multivariate datasets is a particularly difficult problem
which spans across a range of systems, such as quality control in factories, microarrays or proteomic
analyses, identification of features in image analysis, identifying unauthorized access in network
traffic patterns, and detection of changes in ecosystems. Multivariate control charts (MCC) are
popular and sophisticated statistical process control (SPC) methods for monitoring characteristics
of interest and detecting changes in a multivariate process. These methods are divided into
memory-less and memory-type charts which are used to monitor large and small-to-moderate shifts
in the process, respectively. For example, the multivariate χ2 is a memory-less control chart that
uses only the most current process information and disregards any previous observations; it is
typically used where any shifts in the process mean are expected to be relatively large. To increase
the sensitivity of the multivariate process control tool for the detection of small-to-moderate shifts
in the process mean vector, different multivariate memory-type tools that use information from
both the current and previous process observations have been proposed. These tools have proven
very useful for multivariate independent normal or "nearly" normal distributed processes.
Like most univariate control-chart methods, when the process parameters (i.e., the process
mean vector or covariance parameters, or both) are unknown, then MCC methods are based on estimated parameters, and their implementation occurs in two phases. In Phase I (retrospective
phase), a historical reference sample is studied to establish the characteristics of the in-control
state and evaluate the stability of the process. Once the in-control reference sample has been
deemed to be stable, the process parameters are estimated from Phase I, and control chart limits
are obtained for use in Phase II. The Phase II aspect initiates ongoing regular monitoring of the
process. If successive observed values obtained at the beginning of Phase II fall within specified
desired in-control limits, the process is considered to be in control. In contrast, any observed values
during Phase II which fall outside the specified control limits indicate that the process may be out
of control, and remedial responses are then required.
Although conventional MCC are well developed from a statistical point of view, they can be
difficult to apply in modern, data-rich contexts. This serious drawback comes from the fact that
classical MCC plotting statistics requires the inversion of the covariance matrix, which is typically
assumed to be known. In practice, the covariance matrix is seldom known and often empirically
estimated, using a sample covariance matrix from historical data. While the empirical estimate
of the covariance matrix may be an unbiased and consistent estimator for a low-dimensional data
matrix with an adequate prior sample size, it performs inconsistently in high-dimensional settings.
In particular, the empirical estimate of the covariance matrix can lead to in
ated false-alarm rates
and decreased sensitivity of the chart to detect changes in the process.
Also, the statistical properties of traditional MCC tools are accurate only if the assumption
of multivariate normality is satisfied. However, in many cases, the underlying system is not multivariate
normal, and as a result, the traditional charts can be adversely affected. The necessity
of this assumption generally restricts the application of traditional control charts to monitoring industrial processes.
Most MCC applications also typically focus on monitoring either the process mean vector or
the process variability, and they require that the process mean vector be stable, and that the
process variability be independent of the process mean. However, in many real-life processes, the
process variability is dependent on the mean, and the mean is not necessarily constant. In such
cases, it is more appropriate to monitor the coefficient of variation (CV). The univariate CV is the
ratio of the standard deviation to the mean of a random variable. As a relative dispersion measure
to the mean, it is useful for comparing the variability of populations having very different process
means. More recently, MCC methods have been adapted for monitoring the multivariate coefficient
of variation (CV). However, to date, studies of multivariate CV control charts have focused on
power - the detection of out-of-control parameters in Phase II, while no study has investigated
their in-control performance in Phase I. The Phase I data set can contain unusual observations,
which are problematic as they can in
uence the parameter estimates, resulting in Phase II control
charts with reduced power. Relevant Phase I analysis will guide practitioners with the choice of
appropriate multivariate CV estimation procedures when the Phase I data contain contaminated
samples.
In this thesis, we investigated the performance of the most widely adopted memory-type
MCC methods: the multivariate cumulative sum (MCUSUM) and the multivariate exponentially
weighted moving average (MEWMA) charts, for monitoring shifts in a process mean vector when
the process parameters are unknown and estimated from Phase I (chapters 2 and 3). We demonstrate
that using a shrinkage estimate of the covariance matrix improves the run-length performance
of these methods, particularly when only a small Phase I sample size is available. In chapter 4, we investigate the Phase I performance of a variety of multivariate CV charts, considering both
diffuse symmetric and localized CV disturbance scenarios, and using probability to signal (PTS)
as a performance measure.
We present a new memory-type control chart for monitoring the mean vector of a multivariate
normally distributed process, namely, the multivariate homogeneously weighted moving average
(MHWMA) control chart (chapter 5). We present the design procedure and compare the run
length performance of the proposed MHWMA chart for the detection of small shifts in the process
mean vector with a variety of other existing MCC methods. We also present a dissimilarity-based
distribution-free control chart for monitoring changes in the centroid of a multivariate ecological
community (chapter 6). The proposed chart may be used, for example, to discover when an impact
may have occurred in a monitored ecosystem, and is based on a change-point method that does
not require prior knowledge of the ecosystem's behaviour before the monitoring begins. A novel
permutation procedure is employed to obtain the control-chart limits of the proposed charting
test-statistic to obtain a suitable distance-based model of the target ecological community through
time.
Finally, we propose enhancements to some classical univariate control chart tools for monitoring
small shifts in the process mean, for those scenarios where the process variable is observed along
with a correlated auxiliary variable (chapters 7 through 9). We provide the design structure of the
charts and examine their performance in terms of their run length properties. We compare the run
length performance of the proposed charts with several existing charts for detecting a small shift
in the process mean. We offer suggestions on the applications of the proposed charts (in chapters
7 and 8), for cases where the exact measurement of the process variable of interest or the auxiliary variable is diffcult or expensive to obtain, but where the rank ordering of its units can be obtained
at a negligible cost.
Thus, this thesis, in general, will aid practitioners in applying a wider variety of enhanced and
novel control chart tools for more powerful and effcient monitoring of multivariate process. In
particular, we develop and test alternative methods for estimating covariance matrices of some
useful control-charts' tools (chapters 2 and 3), give recommendations on the choice of an appropriate
multivariate CV chart in Phase I (chapter 4), present an efficient method for monitoring small
shifts in the process mean vector (chapter 5), expand MCC analyses to cope with non-normally
distributed datasets (chapter 6) and contribute to methods that allow efficient use of an auxiliary
variable that is observed and correlated with the process variable of interest (chapters 7 through
9)
Monitoring of the BTA Deep Hole Drilling Process Using Residual Control Charts
Deep hole drilling methods are used for producing holes with a high lengthto- diameter ratio, good surface finish and straightness. The process is subject to dynamic disturbances usually classified as either chatter vibration or spiralling. In this work, we propose to monitor the BTA drilling process using control charts to detect chatter as early as possible and to secure production with high quality. These control charts use the residuals obtained from a model which describes the variation in the amplitude of the relevant frequencies of the process. The results showed that chatter is detected and some alarm signals are related to changing physical conditions of the process. --
A Proposed Single EWMA Chart Combining The X And R Charts For A Joint Monitoring Of The Process Mean And Variance [TS156. Y46 2008 f rb].
Dua carta kawalan biasanya digunakan untuk kawalan min proses dan varians proses secara berasingan di industri pengeluaran.
In manufacturing industries, two control charts are usually used to monitor the process mean and the process variance separately
EWMA Chart and Measurement Error
Measurement error is a usually met distortion factor in real-world applications that influences the outcome of a process. In this paper, we examine the effect of measurement error on the ability of the EWMA control chart to detect out-of-control situations. The model used is the one involving linear covariates. We investigate the ability of the EWMA chart in the case of a shift in mean. The effect of taking multiple measurements on each sampled unit and the case of linearly increasing variance are also examined. We prove that, in the case of measurement error, the performance of the chart regarding the mean is significantly affected.Exponentially weighted moving average control chart, Average run length, Average time to signal, Measurement error, Markov chain, Statistical process control
A Comparison Of The Performances Of Various Single Variable Charts.
Control charts are used for process monitoring and improvement in industries. Two charts are usually used in the monitoring of both the mean and variance separately
Monitoring Processes with Changing Variances
Statistical process control (SPC) has evolved beyond its classical applications in manufacturing to monitoring economic and social phenomena. This extension requires consideration of autocorrelated and possibly non-stationary time series. Less attention has been paid to the possibility that the variance of the process may also change over time. In this paper we use the innovations state space modeling framework to develop conditionally heteroscedastic models. We provide examples to show that the incorrect use of homoscedastic models may lead to erroneous decisions about the nature of the process. The framework is extended to include counts data, when we also introduce a new type of chart, the P-value chart, to accommodate the changes in distributional form from one period to the next.control charts, count data, GARCH, heteroscedasticity, innovations, state space, statistical process control
A Technique to compare ewmad2 scheme with different sample sizes
Basically the Exponentially Weighted Moving Average (EWMA) charts were introduced for monitoring the process mean in 1959 by Robert. It is much sensitive in detecting small shifts of mean than Shewhart charts. But lately it was felt that monitoring process mean was not enough in some cases. Then it was essential to introduce EWMA chart for monitoring sample variance and such a chart was introduced by Chen and Gan in 1993. These both EWMA charts can be used to monitor process mean and variance independently. But later it was identified monitoring mean and variance is a bivariate problem. In this series Exponentially Weighted Moving Average Distance square scheme (EWMAD2) was introduced with the claim that the control limits of the schemes are independent of sample size. In this research project the effect of sample size in EWMAD2 scheme is analyzed with the simulated samples with the different sample size and Average Run Lengths. In conclusion it is proved that EWMAD2 scheme is independent of sample size in determining the control limits
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