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A preliminary control chart based on individual observations for detecting a shift in either the mean or variance or both is developed from a likelihood ratio test. The advantages over use of the X control chart and moving range control chart are improved detection of sustained shifts, in addition to improved diagnostic information indicating multiple shifts and whether an out-of-control signal is primarily due to a shift in the mean or variance or a combination. Approximate control limits, determined from simulation, are given for the proposed control chart.
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Sullivan et al. (1996) studied this question.
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