Economic Control of Quality of Manufactured Product.

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

This paper seeks a theoretical basis for determining the optimal parameters of the X-chart under the specified conditions. These parameters are the sample size, the factor determining the spread of the control limits, and the intersample interval. The paper shows how to determine these parameters under sound practical assumptions so that the relevant cost function is minimized. Illustrative examples show how the formulated model can be applied.

Economically optimal determination of the parameters of np-control charts

An approximate cost model for a quality control procedure for two or more related variables is investigated. A method is presented to determine the optimal sample size, interval between samples, and critical region parameter for the Hotelling T2 control chart. This model is a multivariate analog of several well-known models for the univariate XI-chart. It is assumed that only one assignable cause of variation exists and the time between occurrences is exponentially distributed. Numerical results are provided in a particular bivariate case for several values of the cost coefficients. The behavior of the model to variation of the model parameters is discussed.

https://www.jstor.org/stable/info/2629112

Economic Design of T2 Control Charts to Maintain Current Control of a Process

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 ..

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

Section of mathematics and engineering: technological stability in industrial operations*

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Techniques pour une utilisation économique des cartes de contrôle

: This study is concerned mainly with changes in process parameters. For the criteria under consideration, properties of the mean action time, M.A.T., that is, the mean number of samples (including the one at which action is to be taken) between successive actions, is determined, where by action is meant the decision to examine the process for the presence of assignable causes of variation. An exact determination of M.A.T. (mean action time) is found for two important control criteria. The analytical results provide a basis for comparison of the Shewhart standard control chart, the cumulative sum control chart and the Double Limit Control Chart, as well as the Run Control Chart, which are used from time to time on an empirical basis. These ideas may be applied to other control charts where the random variables have different distributions. (Author)

Double limit and run control charts: exact statistical properties,

Section of mathematics and engineering: mathematical, psychological, and engineering aspects of accident phenomena*: i. operational aspects of the accident proneness concept**

Sebastian B. Littauer

Papers

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

Section of mathematics and engineering: technological stability in industrial operations*

Techniques pour une utilisation économique des cartes de contrôle

Double limit and run control charts: exact statistical properties,

Section of mathematics and engineering: mathematical, psychological, and engineering aspects of accident phenomena*: i. operational aspects of the accident proneness concept**