A small electronic device is designed to emit a timing signal of 200.0 milliseconds (ms) duration.  This device is specified as 201.0 + 10.0. In the production of this device, subgroups of six units are taken at periodic intervals and tested.  Xbar and  R  are calculated for each subgroup and used to plot control charts.  The results of inspection of 25 subgroups,  ΣX = 5,000.00  and  ΣR = 277.00.  Assuming that the mean of the process shifts to 196 V dc, compute the Type II Error probability that it will not be detected on the first subgroup drawn after the shift occurs.

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A small electronic device is designed to emit a timing signal of 200.0 milliseconds (ms) duration.  This device is specified as 201.0 + 10.0. In the production of this device, subgroups of six units are taken at periodic intervals and tested.  Xbar and  R  are calculated for each subgroup and used to plot control charts.  The results of inspection of 25 subgroups,  ΣX = 5,000.00  and  ΣR = 277.00. 

  • Assuming that the mean of the process shifts to 196 V dc, compute the Type II Error probability that it will not be detected on the first subgroup drawn after the shift occurs.
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