A Time Truncated Moving Average Chart for the Weibull Distribution

A control chart of monitoring the number of failures is proposed with a moving average scheme, when the life of an item follows a Weibull distribution. A specified number of items are put on a time truncated life test and the number of failures is observed. The proposed control chart has been evaluated by the average run lengths (ARLs) under different parameter settings. The control constant and the test time multiplier are to be determined by considering the in-control ARL. It is observed that the proposed control chart is more efficient in detecting a shift in the process as compared with the existing time truncated control chart. ? 2013 IEEE.11Ysciescopu

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

Control Charts for Poisson Counts based on the Stein-Chen Identity

If monitoring Poisson count data for a possible mean shift (while the Poisson distribution is preserved), then the ordinary Poisson exponentially weighted moving-average (EWMA) control chart proved to be a good solution. In practice, however, mean shifts might occur in combination with further changes in the distribution family. Or due to a misspecification during Phase-I analysis, the Poisson assumption might not be appropriate at all. In such cases, the ordinary EWMA chart might not perform satisfactorily. Therefore, two novel classes of generalized EWMA charts are proposed, which utilize the so-called Stein-Chen identity and are thus sensitive to further distributional changes than just sole mean shifts. Their average run length (ARL) performance is investigated with simulations, where it becomes clear that especially the class of so-called "ABC-EWMA charts" shows an appealing ARL performance. The practical application of the novel Stein-Chen EWMA charts is illustrated with an application to count data from semiconductor manufacturing

A Proposed Double Moving Average (DMA) Control Chart [TS156.8. W872 2007 f rb].

Teknik carta kawalan telah digunakan secara meluas dalam industri untuk mengawal kualiti proses pengeluaran. Carta kawalan dengan ingatan diperkenalkan sebagai alternatif kepada carta Shewhart untuk pengesanan anjakan tetap proses yang kecil. Control chart techniques have been widely used in industries to monitor the quality of manufacturing processes. Memory control charts are introduced as alternatives to the Shewhart charts for quick detections of small sustaining process shifts

Detecting the start of an influenza outbreak using exponentially weighted moving average charts

Background. Influenza viruses cause seasonal outbreaks in temperate climates, usually during winter and early spring, and are endemic in tropical climates. The severity and length of influenza outbreaks vary from year to year. Quick and reliable detection of the start of an outbreak is needed to promote public health measures. Methods. We propose the use of an exponentially weighted moving average (EWMA) control chart of laboratory confirmed influenza counts to detect the start and end of influenza outbreaks. Results. The chart is shown to provide timely signals in an example application with seven years of data from Victoria, Australia. Conclusions. The EWMA control chart could be applied in other applications to quickly detect influenza outbreaks

ARL Evaluation of a DEWMA Control Chart for Autocorrelated Data: A Case Study on Prices of Major Industrial Commodities

The double exponentially weighted moving average (DEWMA) control chart, an extension of the EWMA control chart, is a useful statistical process control tool for detecting small shift sizes in the mean of processes with either independent or autocorrelated observations. In this study, we derived explicit formulas to compute the average run length (ARL) for a moving average of order q (MA(q)) process with exponential white noise running on a DEWMA control chart and verified their accuracy by comparison with the numerical integral equation (NIE) method. The results for both were in good agreement with the actual ARL. To investigate the efficiency of the proposed procedure on the DEWMA control chart, a performance comparison between it and the standard and modified EWMA control charts was also conducted to determine which provided the smallest out-of-control ARL value for several scenarios involving MA(q) processes. It was found that the DEWMA control chart provided the lowest out-of-control ARL for all cases of varying the exponential smoothing parameter and shift size values. To illustrate the efficacy of the proposed methodology, the presented approach was applied to datasets of the prices of several major industrial commodities in Thailand. The findings show that the DEWMA procedure performed well in almost all of the scenarios tested. Doi: 10.28991/ESJ-2023-07-05-020 Full Text: PD