Control charts for a tablet compression process. A pharmaceutical manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The hardness of a sample from each lot of tablets is measured to control the compression process. The process has been operating in control with mean at the target value μ = 11.5 kiloponds (kp) and estimated standard deviation σ = 0.2 kp.

Given Table gives three sets of data, each representing x for 20 successive samples of n = 4 tablets. One set of data remains in control at the target value. In a second set, the process mean μ shifts suddenly to a new value. In a third, the process mean drifts gradually

(a) What are the center line and control limits for an x chart for this process?

(b) Draw a separate chart for each of the three data sets. Mark any points that are beyond the control limits.

(c) Based on your work in part (b) and the appearance of the control charts, which set of data comes from a process that is in control? In which case does the process mean shift suddenly, and at about which sample do you think that the mean changed? Finally, in which case does the mean drift gradually?