320 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
A Binary Control Chart to Detect Small Jumps
The classic N p chart gives a signal if the number of successes in a sequence
of inde- pendent binary variables exceeds a control limit. Motivated by
engineering applications in industrial image processing and, to some extent,
financial statistics, we study a simple modification of this chart, which uses
only the most recent observations. Our aim is to construct a control chart for
detecting a shift of an unknown size, allowing for an unknown distribution of
the error terms. Simulation studies indicate that the proposed chart is su-
perior in terms of out-of-control average run length, when one is interest in
the detection of very small shifts. We provide a (functional) central limit
theorem under a change-point model with local alternatives which explains that
unexpected and interesting behavior. Since real observations are often not
independent, the question arises whether these re- sults still hold true for
the dependent case. Indeed, our asymptotic results work under the fairly
general condition that the observations form a martingale difference array.
This enlarges the applicability of our results considerably, firstly, to a
large class time series models, and, secondly, to locally dependent image data,
as we demonstrate by an example
Evaluation of the Run-Length Distribution for a Combined Shewhart-EWMA Control Chart
A simple algorithm is introduced for computing the run length distribution of a monitoring scheme combining a Shewhart chart with an Exponentially Weighted Moving Average control chart. The algorithm is based on the numerical approximation of the integral equations and integral recurrence relations related to the run-length distribution. In particular, a modified Clenshaw-Curtis quadrature rule is applied for handling discontinuities in the integrand function due to the simultaneous use of the two control schemes.
The proposed algorithm, implemented in R and publicy available, compares favourably with the Markov chain approach originally used to approximate the run length properties of the combined Shewhart-EWMA
Detection Sensitivity of a Modified EWMA Control Chart with a Time Series Model with Fractionality and Integration
Among the many statistical process control charts, the modified exponentially weighted moving average (EWMA) control chart has been designed to swiftly detect a small shift in a process parameter. Herein, we propose two explicit formulas for the average run length (ARL) for integrated moving average (IMA) and fractional integrated moving average (FIMA) models combined with the modified EWMA control chart for time series prediction. The application of the suggested control chart procedures depends on the residuals of the IMA and FIMA models. The performance of the control chart with both models is evaluated by using the ARL. Explicit formulas for the ARL for the two models with the modified EWMA statistic are derived and their precision is compared with the numerical integral equation method. The explicit formulas could accurately predict the true ARL while markedly decreasing the computational processing time compared to the numerical integration method. The capabilities of the IMA and FIMA models with the modified EWMA control chart were studied by varying g times the last term and exponential smoothing parameter λ, with the relative mean index being used to evaluate these situations. The results show that the modified EWMA control chart with either model performed better than the original EWMA control chart. Furthermore, the modified EWMA control chart with either model was highly efficient when g increased and λ was small. Two applications involving energy commodity prices are used to illustrate the efficacies of the proposed approaches, the results of which were in accordance with the experimental study. Doi: 10.28991/ESJ-2022-06-05-015 Full Text: PD
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