Problem 1 Samples of n=4 items each are taken from a manufacturing process at regular intervals. A quality characteristic is measured, and x-bar and R values are calculated for each sample. After 25 samples, we have: X-bar = 107.5 R = 12.5 Assume that the quality characteristic is normally distributed. a) Compute control limits for the x-bar and R control charts b) Estimate the process mean and standard deviation c) Assuming that the process is in control, what are the natural tolerance limits of the process? d) If the specifications limits are 4.4 + 0.2. What is the process capability? Is the process capable of meeting the specifications? e) Assuming that if any item exceeds the upper specification limit it can be reworked, and if it is below the lower specification limit, it must be scrapped, what percent scrap and rework is the process producing? f) If the unit cost of scrap and rework are $2.4 and $0.75, respectively, find the total daily cost of scrap and rework. g) If a process average shifts to 4.5 mm, what is the impact on the proportion of scrap and rework produced