The usual practice in using a control chart to monitor a process is to take samples from the process with fixed sampling intervals. This article considers the properties of the chart when the sampling interval between each pair of samples is not fixed but rather depends on what is observed in the first sample. The idea is that the time interval until the next sample should be short if a sample shows some indication of a change in the process and long if there is no indication of a change. The proposed variable sampling interval (VSI) chart uses a short sampling interval if is close to but not actually outside the control limits and a long sampling interval if is close to target. If is actually outside the control limits, then the chart signals in the same way as the standard fixed sampling interval (FSI) chart. Properties such as the average time to signal and the average number of samples to signal are evaluated. Comparisons between the FSI and the VSI charts indicate that the VSI chart is substantially ...

X charts with variable sampling intervals

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.

Nonparametric quality control charts based on the sign statistic

In the last three decades several control chart procedures were developed. Prominent among these, are the Cumulative Sum, Economic design of X-bar control charts, Acceptance and Multi-Characteristic charts. This article presents description and analysis..

Recent Developments in Control Chart Techniques

Under the normality assurnption. four univariate exponentially nioving average single control charts are proposed and they are designed to monitor simultaneously both the process mean and the process variability The perforniances of these four charts are evaluated by comparing their average run lengths aniong tliemselves as well as to two other competing combination charts. Based on thcl cornparison of the six ~inivariate charts. a multivariate exponentially nioving average single control chart is deveioped as an extension of one of the best univariatt? charts. This chart perfornis better than the combination of the two widely iisctl riiultivariate chürts when small changes are of interest. In dealing with positively-skewed distributed data. the direct logarit hniic trarisformation may result in a control chart wi th inappropriate control paranieters in the application of quality control. When a specific interval for the lognornial mean is given. a new method is introduced to set up two control charts and these two charts can monitor a process for which the underlying distribution of the quality characteristic is lognormal.

Contributions to qualimetry

Some properties of control procedures with variable sampling intervals (VSI) have been investigated in recent years by Amin, Renolds et al, and others. Such procedures have been shown to be more efficient when compared to the corresponding fixed sampling interval (FSI) charts with respect to the Average Time to Signal (ATS) when the Average Run Length (ARL) values for 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 (VSI). This problem is being addressed in this article, and improved switching rules are presented and evaluated for Shewhart, CUSUM, and EWMA control procedures. The proposed rules considerably reduce the average number of switches between the sampling intervals and also improve the ATS properties of the control procedures when compared to the conventional variable sampling interval procedures

Improved switching rules in control procedures using variable sampling intervals

The Shewhart control chart for means can be made more sensitive to small changes by adding a pair of warning limits, located inside the action limits, and taking action when a run of a specified number of consecutive means falls between the warning and ..

Joachim I. Weindling

Papers

Mean Action Time of the X-Bar Control Chart with Warning Limits