DS 16.3.1 contains the sample means i and the sample ranges ri of samples of size n = 4 of a measurement of interest collected at k = 20 distinct time points from a production process.
(a) Construct an -chart and an R-chart.
(b) Is there any evidence that the process was out of control while the data values were collected? Should any of the samples be removed from the data set?
(c) If the control charts are used for monitoring future production runs, what conclusion would you draw if a sample x1 = 86.1, x2 = 99.2, x3 = 94.5, and x4 = 90.7 is obtained?
(d) What if x1 = 91.5, x2 = 78.0, x3 = 86.5, and x4 = 82.4?
(e) What if x1 = 95.3, x2 = 92.1, x3 = 89.6, and x4 = 90.1?
(f) What if x1 = 99.2, x2 = 93.8, x3 = 96.1, and x4 = 94.2?