A double exponentially weigiited moving average control procedure with variable sampling intervals

Shewhart, cumulative sum (CUSUM), and exponentially weighted moving average (EWMA) control procedures with variable sampling intervals (VSI) have been investigated in recent years for detecting shifts in the process mean. Such procedures have been shown to be more efficient when compared with the corresponding fixed sampling interval (FSI) charts with respect to the average time to signal (ATS) when the average run length (ARL) values of both types of procedures are held equal. Frequent switching between the different sampling intervals can be a complicating factor in the application of control charts with variable sampling intervals. In this article, we propose using a double exponentially weighted moving average control procedure with variable sampling intervals (VSI-DEWMA) for detecting shifts in the process mean. It is shown that the proposed VSI-DEWMA control procedure is more efficient when compared with the corresponding fixed sampling interval FSI-DEWMA chart with respect to the average time to signal (ATS) when the average run length (ARL) values of both types of procedures are held equal. It is also shown that the VSI-DEWMA procedure reduces the average number of switches between the sampling intervals and has similar ATS properties as compared to the VSI-EMTMA control procedure     

An alternative approach for analysis of performance of one-sided cusum charts with variable sampling intervals

An alternative approach for analyzing performance of one-sided Cusum charts with variable sampling intervals (VSI) is proposed. In this approach, a Markov chain with some dummy states is used. By this approach some dynamic performance measures of the VSI Cusum charts, such as the distribution of time to signal and the average time to signal against a change-point, can be determined. Some numerical results are shown, and from these results the dynamic performance of VSI Cusum charts is discussed.     

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.     

Nonparametric quality control charts based on the sign statistic

Nonparametric control chart are presented for the problem of detecting changes in the process median (or mean), or changes in the process variability when samples are taken at regular time intervals. The proposed procedures are based on sign-test statistics computed for each sample, and are used in Shewhart and cumulative sum control charts. When the process is in control the run length distributions for the proposed nonparametric control charts do not depend on the distribution of the observations. An additional advantage of the non-parametric control charts is that the variance of the process does not need to be established in order to set up a control chart for the mean. Comparisons with the corresponding parametric control charts are presented. It is also shown that curtailed sampling plans can considerably reduce the expected number of observations used in the Shewhart control schemes based on the sign statistic.     

Adjusted-loss-function charts with variable sample sizes and sampling intervals

Recent research has shown that the control charts with adaptive features are quicker than the traditional static Shewhart charts in detecting process shifts. This article presents the design and implementation of a control chart based on Adjusted Loss Function (AL) with Variable Sample Sizes and Sampling Intervals (VSSI). This single chart (called the VSSI AL chart) is able to monitor the process shifts in mean and variance simultaneously. Our studies show that the VSSI AL chart is not only easier to design and implement than the VSSI X¯ & S (or X¯ & R) charts, but is also 10% more effective than the latter in detecting the process shifts from an overall viewpoint.     

Double sampling |S| control chart with variable sample size and variable sampling interval

This study presents a control chart for monitoring shifts in the covariance matrix of a multivariate normally distributed process. This chart combines the double sampling, variable sample size and variable sampling interval features, and is called the DSVSSI |S| chart. A Markov chain approach is developed to design the DSVSSI |S| chart, by minimizing the average time to signal (ATS), for a specified shift size in the covariance matrix. The DSVSSI |S| chart has a better ATS performance compared to other existing charts. An example is given to illustrate the operation of the DSVSSI |S| chart.     

Optimal design of the variable sampling size and sampling interval variable dimension T2 control chart for monitoring the mean vector of a multivariate normal process

This paper develops the algorithm for the optimization designs of the adaptive T² Control Chart for Monitoring the Mean Vector of a Multivariate Normal Process. It includes the variable sample size, variable sampling interval and variable dimensional chart. The VDT² control chart performs well for moderate and large shifts in the mean vector. However, its performance for small shifts is poor. To improve the chart's performance in detecting such shifts, we propose the application of the variable sample size and sampling interval technique to the VDT² control chart, resulting in the VSSIVDT² control chart.     

Monitoring the coefficient of variation using a variable sample size and sampling interval control chart

This article proposes a CV chart by using the variable sample size and sampling interval (VSSI) feature to improve the performance of the basic CV chart, for detecting small and moderate shifts in the CV. The proposed VSSI CV chart is designed by allowing the sample size and the sampling interval to vary. The VSSI CV chart's statistical performance is measured by using the average time to signal (ATS) and expected average time to signal (EATS) criteria and is compared with that of existing CV charts. The Markov chain approach is employed in the design of the chart.     

Monitoring prespecified changes in linear profiles using control charts with supplementary runs rules

In profile monitoring, some methods have been developed to detect the unspecified changes in the profiles. However, detecting changes away from the “normal” profile toward one of several prespecified “bad” profiles is one possible and challenging purpose. In this article, control charts with supplementary runs rules are developed to detect the prespecified changes in linear profiles. A control chart is first developed based on the Student's t-statistic in t test, and two runs rules are then supplemented to this chart, respectively. Simulation studies show that the proposed control schemes are effective and stable. Moreover, the control schemes are better than the existing alternative charts when the number of observations per sample profile is large. Finally, two illustrative examples indicate that our proposed schemes are effective and easy to be implemented.     

A control chart for monitoring process variation using multiple dependent state sampling

A control chart for monitoring process variation by using multiple dependent state (MDS) sampling is constructed in the present article. The operational formulas for in-control and out-of-control average run lengths (ARLs) are derived. Control constants are established by considering the target in-control ARL at a normal process. The extensive ARL tables are reported for various parameters and shifted values of process parameters. The performance of the proposed control chart has been evaluated with several existing charts in regard of ARLs, which empowered the presented chart and proved far better for timely detection of assignable causes. The application of the proposed concept is illustrated with a real-life industrial example and a simulation-based study to elaborate strength of the proposed chart over the existing concepts.     

EVVMA and cusum control charts in the presence of correlation

The statistical properties of control charts are usually evaluated under the assumption that the observations from the process are independent. For many processes however, observations which are closely spaced in time will be correlated. This paper considers EWMA and CUSUM control charts for the process mean when the observations are from an AR(1) process with additional random error. This simple model may be a reasonable model for many processes encountered in practice. The ARL and steady state ARL of the EWMA and CUSUM charts are evaluated numerically using an integral equation approach and a Markov chain approach. The numerical results show that correlation can have a significant effect on the properties of these charts. Tables are given to aid in the design of these charts when the observations follow the assumed model.     

Modified Group Runs Control Charts to Detect Increases in Fraction Non Conforming and Shifts in the Process Mean

The nonparametric two-sample bootstrap is employed to compute uncertainties of measures in receiver operating characteristic (ROC) analysis on large datasets in areas such as biometrics, and so on. In this framework, the bootstrap variability was empirically studied without a normality assumption, exhaustively in five scenarios involving both high- and low-accuracy matching algorithms. With a tolerance 0.02 of the coefficient of variation, it was found that 2000 bootstrap replications were appropriate for ROC analysis on large datasets in order to reduce the bootstrap variance and ensure the accuracy of the computation.