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Statistical Process Control monitoring of the ratio Z of two normal variables X and Y has received too little attention in quality control literature. Several applications dealing with monitoring the ratio Z can be found in the industrial sector, when quality control of products consisting of several raw materials calls for monitoring their proportions (ratios) within a product. Tables about the statistical performance of these charts are still not available. This paper investigates the statistical performance of a Phase II Shewhart control chart monitoring the ratio of two normal variables in the case of individual observations. The obtained results show that the performance of the proposed chart is a function of the distribution parameters of the two normal variables. In particular, the Shewhart chart monitoring the ratio Z outperforms the ( p = 2) multivariate T2 control chart when a process shift affects the in-control mean of X or, alternatively, of Y and the correlation among X and Y is high and when the in-control means of X and Y shift contemporarily to opposite directions. The sensitivity of the proposed chart to a shift of the in-control dispersion has been investigated, too. We also show that the standardization of the two variables before computing their ratio is not a good practice due to a significant loss in the chart's statistical performance. An illustrative example from the food industry details the implementation of the ratio control chart. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes a Variable Sampling Interval version of the Fixed Sampling Interval S²-EWMA control chart developed by Castagliola (2004) and dedicated to the monitoring of the sample variance of a process. In this paper, we explain how the various parameters of this VSI S²-EWMA control chart can be computed and how the use of the VSI feature significantly improves the statistical efficiency of FSI S²-EWMA chart, thus representing an effective tool in the detection of process out-of-control conditions. An optimal design strategy based on the Average Time to Signal (ATS) is presented and a comparison with the PSI procedure is performed. [ABSTRACT FROM AUTHOR]

In this paper, improved Shewhart control charts based on hybrid adaptive and run rule schemes are introduced to enhance the statistical performances of the traditional static scheme, designed with consideration given to the fixed values of sample size, the width of the control limits and the sampling frequency. The proposed hybrid adaptive schemes consider both variable sampling interval and variable sample size combined with run rules. The objective of this research is to develop a statistical comparison between adaptive schemes, charts with run rules and hybrid adaptive schemes with run rules to help decision-makers in the selection of the best performing chart for an expected value of shift in the mean of a controlled parameter. An extensive set of numerical results is presented to test the effectiveness of the proposed models in detecting small and moderate shifts in the process mean. The optimal statistical designs of the charts are obtained through a heuristic algorithm, properly modified to cope with the problem. [ABSTRACT FROM AUTHOR]