Control charts for and R are maintained on a process. After 20 preliminary subgroups (samples) each of size 3 are evaluated, you have the following data:

= 5,502 and = 60

a) Compute the control limits for the and R control charts. (Hint: first compute the grand mean and the average range .)

b) Assume that all points on both charts plot within the control limits (i.e. the and R charts are in statistical control), give an estimate of the (unknown) process mean and an estimate of the (unknown) process standard deviation .

c) If the specification limits on this product are 275 6, what are your conclusions regarding the ability of the process to produce items conforming to specifications? That is, estimate the potential capability of the process and the actual process capability .

d) Assuming that if an item exceeds the upper specification limit it can be reworked, and if it is below the lower specification limit it must scrapped, what percentage scrap and rework is the process now producing? (Hint: Assume that the quality characteristic in question is normally distributed. Use the results of part (b), the normal distribution and the normal curve areas to compute this percentage).

e)Make suggestions as to how the process performance could be improved