17.15 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 in order to control the compression process. The TABLE 17.4 Three sets of x’s from 20 samples of size 4 Sample Data set A Data set B Data set C 1 11.602 11.627 11.495 2 11.547 11.613 11.475 3 11.312 11.493 11.465 4 11.449 11.602 11.497 5 11.401 11.360 11.573 6 11.608 11.374 11.563 7 11.471 11.592 11.321 8 11.453 11.458 11.533 9 11.446 11.552 11.486 10 11.522 11.463 11.502 11 11.664 11.383 11.534 12 11.823 11.715 11.624 13 11.629 11.485 11.629 14 11.602 11.509 11.575 15 11.756 11.429 11.730 16 11.707 11.477 11.680 17 11.612 11.570 11.729 18 11.628 11.623 11.704 19 11.603 11.472 12.052 20 11.816 11.531 11.905 process has been operating in control with mean at the target value μ = 11.5 and estimated standard deviation σ = 0.2. Table 17.4 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 x chart for each of the three data sets. Mark any points that are beyond the control limits.

(c) Based on your work in

(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?