1. X-bar and R charts are maintained on a certain quality characteristic based on a subgroup size of 4. The specifications require that the quality characteristic must be between 345 and 355 lb. On a certain day, data for 25 subgroups of size 4 were collected. ∑X-bar is found to be 8,745.2 and ∑R is found to be 62.8. Assume that the process was in statistical control that day.
a) Calculate the 3-sigma control limits for the X-bar and R control charts
b) If the mean of the process shifts to 347 lb the next day, compute the probability that the shift will not be detected on the X-bar chart on the first subgroup plotted after the shift takes place. Assume no change in Ợ
c) Assuming normal distribution of process output, what proportion of nonconforming units would be produced at this new value of the mean.

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