A variable sampling interval EWMA chart for attributes

We propose a variable sampling interval exponentially weighted moving average (VSI c EWMA) chart for the average number of nonconformities in the sample, with the objective of improved detection of small to moderate increases in the process nonconformities rate. Using a Markov chain model for the calculations, we obtain optimal designs for this chart as well as for the fixed sampling interval c EWMA chart and compare the performances of the two control schemes in terms of their expected times to signal an out-of-control condition. The designs are optimal in the sense that they minimize the expected delay in the detection of upward shifts of a specified magnitude in the process nonconformities rate, while keeping the false alarm rate and the average sampling frequency at specified levels. The results reveal considerable gains in detection speed with the use of the VSI scheme. The optimal parameters found for each case are tabulated and may be used directly in practice. The results of the analysis, including the optimal design parameters tabulated, can also be extended to a VSI np EWMA chart for improved detection of small to moderate increases in the fraction nonconforming of the process provided that in-control fraction nonconforming is small.

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