Raid W. Amin

X charts with variable sampling intervals

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 ...

CUSUM charts with variable sampling intervals

A standard cumulative sum (CUSUM) chart for controlling the process mean takes samples from the process at fixed-length sampling intervals and uses a control statistic based on a cumulative sum of differences between the sample means and the target value. This article proposes a modification of the standard CUSUM scheme that varies the time intervals between samples depending on the value of the CUSUM control statistic. The variable sampling interval (VSI) CUSUM chart uses short sampling intervals if there is an indication that the process mean may have shifted and long sampling intervals if there is no indication of a change in the mean. If the CUSUM statistic actually enters the signal region, then the VSI CUSUM chart signals in the same manner as the standard CUSUM chart. A Markov-chain approach is used to evaluate properties such as the average time to signal and the average number of samples to signal. Results show that the proposed VSI CUSUM chart is considerably more efficient than the standard CUS...

Exponentially weighted moving average control schemes with variable sampling intervals

The idea of using non-constant sampling intervals has been of interest in quality control applications since it was first suggested for the “skip-lot sampling plan” of Dodge. Recent interest has focused on the use of variable sampling interval (VSI) control schemes. VSI control schemes use a short sampling interval is given

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.

A robustness study of X-bar charts with variable sampling intervals

Recent theoretical studies have shown that, for all but very large process shifts, control charts using variable sampling interval (VSI) schemes are more efficient in their detection of shifting processes than the more conventional fixed sampling interv..

Improved switching rules in control procedures using variable sampling intervals

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

EWMA Control Charts for the Smallest and Largest Observations

A proposal is made for an exponentially weighted moving average (EWMA) control chart based on the smallest (Min) and largest (Max) observations in each simple. This MaxMin EWMA chart shows which parameters have increased or decreased when there is a ch..

Epidemiologic mapping of Florida childhood cancer clusters

Childhood cancer remains the leading cause of disease‐related mortality for children. Whereas, improvement in care has dramatically increased survival, the risk factors remain to be fully understood. The increasing incidence of childhood cancer in Florida may be associated with possible cancer clusters. We aimed, in this study, to identify and confirm possible childhood cancer clusters and their subtypes in the state of Florida.

The switching behavior of charts with variable sampling intervals

In a variable sampling interval control scheme the time interval between successive samples is allowed to vary depending on what is being observed from the data. It has been the practice to compare the average time to signal and the average run length of variable sampling interval schemes and the corresponding control procedures with fixed sampling intervals. Thus far design tables for control charts with variable sampling intervals have not considered the effect of the design parameters on the switching behavior of such control procedures. Frequent switches between the different sampling intervals can be a complicating factor in the application of control charts with variable sampling intervals. The problem of switches is addressed in this article and improved switching rules are presented and evaluated for Shewhart control procedures. Expressions for the average number of switches and the average time to signal are obtained. The proposed runs rules considerably reduce the average number of switches betw...

A nonparametric exponentially weighted moving average control scheme

A common assumption when evaluating the properties of Exponentially Weighted Moving Average (EWMA) control procedures for controlling the process mean is the observations are normal with known variance. In this article we propose a nonparametric control procedure that can be used when the underlying distribution is not know there is not enough information on the variance or shape of the distribution. Its average run length properties are less affected than the corresponding parametric EWMA procedure when autocorrelation between the observations is present. The procedure nonparametric EWMA procedure is based on Wilcoxon signed-rank statistics ranking is within groups. Our simulation results show that the proposed control procedure is less efficient than the parametric -EWMA procedure when the distribution is not and it can be considerably more efficient than the parametric procedure for heavy- distributions. The proposed procedure is insensitive to misspecification of the van and its ARL properties of the ...