Hand break cable defects. In Control Engineering Practice (March 2013), researchers demonstrated the use of a p-chart for monitoring defects in new automobile hand break cables. A sample of 20 hand break cables were selected off the manufacturing line each day for 100 consecutive days, and the daily numbers of defective cables were determined. On the following days, 1 defect was found: days 2, 3, 14, 18, 27, 28, 29, 32, 41, 44, 55, 57, 66, 69, 71, 73, 81, 83, 84, and 98. On the following days, 2 defects were found: days 12, 38, 51, 62, and 93. The remaining days had no discovered defects.

a. Find the center line for a p-chart of the data.

b. Find the upper control limit (UCL) for a p-chart of the data.

c. Find the lower control limit (LCL) for a p-chart of the data.

d. Plot the daily defective rate on the p-chart. Does the process appear to be out of control?

e. When the true defective rate is very small (near 0), the researchers showed that adjustments need to be made to the control limits of the p-chart. The formulas for the adjusted control limits are as follows: UCL* = UCL + 411 - 2p2 >3n and LCL* = LCL + 411 - 2p2 >3n, where p is the true defective rate and n is the sample size. Assuming the true dewfective rate is p = .015, compute the adjusted control limits and form the adjusted p-chart of the data. Now does the process appear to be out of control?