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 the process is in control and that variation in the product follows a normal distribution, what proportion of defective product is being made ?

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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 the process is in control and that variation in the product follows a normal distribution, what proportion of defective product is being made ?
Expert Solution
Step 1

given data 

 N=25

X =5000.00

R=277.00

R ΣR 277 25 11.08 η

ΣΧ 5000 X = 200 η 25

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