Variable sampling interval run sum median charts with known and estimated process parameters

Abstract The variable sampling interval run sum (VSI RS) median chart with known and estimated process parameters are proposed for efficiently monitoring the process mean. The construction, optimal designs, performance assessment and implementation of the VSI RS median chart, are discussed in this paper. The VSI RS median chart is compared with the Shewhart median, run sum median and exponentially weighted moving average median charts, in terms of average time to signal and standard deviation of the time to signal criteria, when process parameters are known, while the average of the average time to signal criterion is used when process parameters are estimated. For both cases of known and estimated process parameters, the VSI RS median chart is found to outperform the Shewhart median chart for all sizes of mean shifts and the exponentially weighted moving average median chart for moderate and large mean shifts. When process parameters are estimated, the standard deviation of the average time to signal criterion is used to evaluate the average of the average time to signal performance of the VSI RS median chart, when the process is in-control. Based on the standard deviation of the average time to signal criterion, the number of Phase-I samples required by the chart to have an in-control average of the average time to signal performance close to its in-control average time to signal performance is recommended.

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