Producing aluminum plates with holes. A French company produces aluminum plates in which holes are bored using a drilling machine. The inner diameter of each hole is designed to be 19.1 millimeters. To monitor the drilling process, 24 plates were sampled—one each hour—from the production line. Four holes are randomly selected from each plate and the diameter of each hole measured. Some of the data, published in Quality and Reliability Engineering International (June 2020), are presented in the table on the next page.

a. For each plate, compute the mean and range of the four diameters.

b. Use the information, part

a, to construct an x-chart.

c. What does the chart suggest about the stability of the hole drilling process (i.e., whether the process is in or out of statistical control)? Justify your answer.

d. Should the control limits be used to monitor future process output? Explain Plate Hole 1 Hole 2 Hole 3 Hole 4 1 19.101 19.103 19.103 19.102 2 19.101 19.104 19.106 19.105 3 19.107 19.107 19.104 19.101 4 19.101 19.107 19.101 19.101 5 19.106 19.102 19.101 19.101 6 19.104 19.103 19.103 19.102 7 19.105 19.108 19.102 19.103 8 19.1 19.101 19.106 19.105 9 19.105 19.104 19.1 19.103 10 19.1 19.1 19.103 19.099 11 19.104 19.104 19.103 19.103 12 19.101 19.103 19.106 19.1 13 19.101 19.099 19.103 19.1 14 19.105 19.103 19.103 19.104 15 19.105 19.104 19.097 19.1 16 19.108 19.105 19.099 19.103 17 19.102 19.096 19.101 19.1 18 19.102 19.102 19.104 19.102 19 19.103 19.102 19.101 19.104 20 19.105 19.099 19.102 19.097 21 19.104 19.103 19.102 19.101 22 19.103 19.099 19.107 19.101 23 19.102 19.104 19.101 19.104 24 19.1 19.104 19.105 19.105 Source: Sabahno, H., Castagliola, P., & Amiri, A. “A variable parameters multivariate control chart for simultaneous monitoring of the process mean and variability with measurement errors”, Quality and Reliability Engineering International, Vol. 36, No. 4, June 2020 (Table 11).