Dyeing yarn: special causes. The process described in Exercise 27.15 goes out of control. Investigation finds that a new type of yarn was recently introduced. The pH in the kettles is influenced by both the dye liquor and the yarn. Moreover, on a few occasions a faulty valve on one of the kettles had allowed water to enter that kettle; as a result, the yarn in that kettle had to be discarded. Which of these special causes appears on the s chart and which on the chart? Explain your answer.

Dyeing yarn. The unique colors of the cashmere sweaters your firm makes result from heating undyed yarn in a kettle with a dye liquor. The pH (acidity) of the liquor is critical for regulating dye uptake and hence the final color. There are 5 kettles, all of which receive dye liquor from a common source. Twice each day, the pH of the liquor in each kettle is measured, giving samples of size 5. The process has been operating in control with µ= 4.22 and σ= 0.127.

(a) Give the center line and control limits for the s chart.
(b) Give the center line and control limits for the chart.