The Precision Machining Company makes hand-held tools on an assembly line that produces one product every minute. On one of the products, the critical quality dimension is the diameter (measured in thousandths of an inch) of a hole bored in one of the assemblies. Management wants to detect any shut in the process average diameter from 0.015in. Management considers the variance in the process to be in control. Historically the average range has been 0.002 in., regardless of the process average. Design an x-chart to control this process, with a center line at 0.015 in. and the control limits set at three sigma€™s from the center line.
Management provided the results of 80 minutes of output from the production line, as shown in Table. During these 80 minutes, the process average changed once. All measurements are in thousandths of an inch.
SAMPLE DATA FOR PRECISION MACHINING COMPANY

a. Set up an x-chart with n = 4. The frequency should be sample four and then skip four. Thus, your first sample would be for minutes 1-4, the second would be for minutes 9€”12 and so on. When would you stop the process to check for a change in the process average?
b. Set up an x-chart with n = 8. The frequency should be sample eight and then skip four. When would you stop the process now? What can you say about the desirability of large samples on a frequent samplinginterval?

Minutes 1-1215 16 18 146 17 15 14413 167 13-24 15 16 16 4 14 13 14 116 117 25-36 14 13 5 715 16 15 1415 16 17 37-48 1816 1616 14 17 18 19 15 16 15 49-60 1 1614 15 1416 15 1718 14 61-72 15 67 18 15 14 146 15 718 73-01616 17 18 151417 Diameter (thousandths of an inch)