2. A case study deals with the length at which a cap is electronically placed on syringes manufactured in a Midwestern pharmaceutical plant.7 The cap should be tacked at an approximate length of 4.95 in. If the length is less than 4.92 in. or larger than 4.98 in., the syringe must be scrapped. In total, 47 samples of size 5 were taken, with the first 15 samples used for calibration. After sample 32, the maintenance technician was called to adjust the machine. The data (transformed by subtracting 4.9 and multiplying times 100) can be found in SqcSyringeL.txt.

(a) Use commands similar to those given in Example 13.2-2 to construct a 3σ X chart, using the estimator!σ2 given in (13.2.5). What does the chart suggest regarding the effect of the adjustment made after the 32nd sample? Has the adjustment brought the process back in control?

(b) Use a command similar to (13.2.8) to delete the second subgroup and re-construct the 3σ X chart with the new control limits. Have your conclusions in part

(a) changed?

(c) Repeat parts

(a) and

(b) using the estimator !σ1 given in (13.2.5). Have the conclusions from parts

(a) and

(b) changed?

(d) Use commands similar to those given in Example 13.2-1(b), and upper and lower specification limits of 4.92 and 4.98, to estimate the process yield after the adjustment made. (Hint. Import the data into the R data frame syr, and transform it back to the original scale by x=syr$x/100+4.9. Use sum(x[161:235]>=4.92&x[161:235]<=4.98).)