17.14 Control limits for a dyeing process. 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 five 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 a sample of size 5. The process has been operating in control with

μ=3.648 and

σ=0.182 .

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

b. Give the center line and control limits for the x¯ chart.