One of the operations in a plant consists of thread-grinding a fitting for an aircraft hydraulic system. To monitor the process, a production supervisor randomly sampled five fittings for each hour, for a period of 20 hours, and measured the pitch diameters of the threads. The measurements, expressed in units of .0001 inch in excess of .4000 inch, are shown in the table. (For example, the value 36 represents .4036 inch.)

a. Construct an R-chart to monitor the variation in pitch diameter. Is the process in control?

b. Modify the control limits on the R-chart so that it can be applied to future data.

c. Construct x̅-chart for the process. Does the process mean appear to be in control?

d. Eliminate the points that fall outside the control limits and recalculate their values. Would you recommend using these modified control limits for future data?

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THREADS Hour Pitch Diameters of Threads 1 36 35 34 33 32 31 31 34 32 30 3 30 30 32 30 32 4 32 33 33 32 35 5 32 34 37 37 35 6. 32 32 31 33 33 7 33 33 36 32 31 8 23 33 36 35 36 9 43 36 35 24 31 10 36 35 36 41 41 11 34 38 35 34 38 12 36 38 39 39 40 13 36 40 35 26 33 14 36 35 37 34 33 15 30 37 33 34 35 16 28 31 33 33 33 17 33 30 34 33 35 18 27 28 29 27 30 19 35 36 29 27 32 20 33 35 35 39 36