In the book Tools and Methods for the Improvement of Quality, Gitlow, Gitlow. Oppenheim. and Oppenheim discuss a resort hotel's efforts to improve service by reducing variation in the time it takes to clean and prepare rooms. In order to study the situation, five rooms are selected each day for 25 consecutive days, and the time required to clean and prepare each room is recorded. The data obtained are given in Table 17.6.

a. Calculate the subgroup mean x̅̅ and range R for each of the first two subgroups.

b. Show that x̅̅ = 15.9416 minutes and that  = 2.696 minutes.

c. Find the control chart constants A₂ and DA for the cleaning and preparation time data. Does D, exist? What does this say?

d. Find the center line and control limits for the x̅ chart for these data.

e. Find the center line and control limit for the R chart for these data.

f. Set up (plot) the x̅ and R charts for the cleaning time data

g. Are the x̅ and R charts in control? Explain.