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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
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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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